matrix template class

#ifndef MATRIX_H
#define MATRIX_H
#include <vector>
//#include <debugapi.h>
#include <ostream>

template <class T>
class matrix
{
    std::vector<std::vector<T>> matrix_;

    //util functions
    static T& prod_of_sum (const std::vector<T>& a, const std::vector<T>& b)
    {
        auto result = new T(0);

        for (size_t i = 0; i < a.size(); i++)
            *result += a[i] * b[i];

        return *result;
    }

    static std::vector<T>& get_column(matrix& obj, const size_t& column_number)
    {
        const auto column = new std::vector<T>;
        column->resize(obj.n());

        for (size_t i = 0; i < obj.n(); i++)
            (*column)[i] = obj[i][column_number];

        return *column;
    }

public:
    explicit matrix(const std::vector<std::vector<T>> matrix)
    {
        matrix_ = std::move(matrix);
    }

    explicit matrix(const std::vector<T> matrix)
    {
        matrix_.resize(1);
        matrix_[0] = std::move(matrix);
    }

    matrix(const T** matrix, const size_t n)
    {

        matrix_.resize(n);
        for (size_t i = 0; i < n; i++)
            matrix_[i].resize(n);

        for (size_t i = 0; i < n; i++)
        {
            for (size_t j = 0; j < n; j++)
                matrix_[i][j] = matrix[i][j];
        }

    }

    matrix(const T** matrix, const size_t n, const size_t m)
    {

        matrix_.resize(n);
        for (size_t i = 0; i < n; i++)
            matrix_[i].resize(m);

        for (size_t i = 0; i < n; i++)
        {
            for (size_t j = 0; j < m; j++)
                matrix_[i][j] = matrix[i][j];
        }

    }

    matrix(const size_t& n, const size_t& m)
    {
        matrix_.resize(n);

        for (size_t i = 0; i < n; i++)
            matrix_[i].resize(m);

        for (auto& row : matrix_)
            for (auto& element : row)
                element = 0;

    }

    matrix(const matrix& other)
        : matrix_(other.matrix_)
    {
    }

    matrix(matrix&& other) noexcept
        : matrix_(std::move(other.matrix_))
    {
    }

    ~matrix() = default;

    matrix& operator=(const matrix& other)
    {
        if (this == &other)
            return *this;
        matrix_ = other.matrix_;
        return *this;
    }

    matrix& operator=(matrix&& other) noexcept
    {
        if (this == &other)
            return *this;
        matrix_ = std::move(other.matrix_);
        return *this;
    }

    void set_ones()
    {
        try
        {

            if (n == m)
                throw std::exception("This is not a square matrix, try standart set method");

            for (size_t i = 0; i < n(); i++)
                matrix_[i][i] = 1;

        } catch (std::exception& e)
        {
            //OutputDebugStringA(e.what());
        }
    }

    void clear()
    {
        for (auto& row : matrix_)
            for (auto& element : row)
                element = 0;
    }

    void set(const std::vector<T>& array)
    {
        size_t i = 0;
        size_t j = 0;

        for (auto& element : array)
        {
            matrix_[i][j] = element;
            if (j < m())
                j++;
            else
            {
                i++;
                j = 0;
            }
        }
    }

    size_t m(){
        return
            matrix_[0].size();
    }

    size_t n()
    {
        return
            matrix_.size();
    }

    matrix& transpose()
    {
        auto transposed_matrix = new matrix<T>(m(), n());

        for (size_t i = 0; i < n(); i++)
            for (size_t j = 0; j < m(); j++)
                (*transposed_matrix)[j][i] = (*this)[i][j];

        return *transposed_matrix;
    }

    friend double det(matrix matr)
    {
        size_t n = matr.n();
        const size_t m = matr.m();

        if (m == 1)
        {
            return matr[0][0];
        }
        if (m == 2)
        {
            return matr[0][0] * matr[1][1] - matr[0][1] * matr[1][0];
        }

        double determinant = 0;
        int degree = 1;

        std::vector<std::vector<T>> minor(n);
        for (size_t i = 0; i < n - 1; i++)
            minor.resize(m - 1);

        for (size_t j = 0; j < n - 1; j++)
        {
            minor = get_matrix_without_row_column(matr, 0, j);
            determinant = determinant + matr[0][j] * static_cast<T>(degree) * det(matrix(minor));
            degree = -degree;
        }

        return determinant;

    }

    matrix& inv()
    {

        return
            this->transpose() * (1 / det(*this));

    }

    friend bool operator==(matrix& lhs, matrix& rhs)
    {
        if (lhs.m() != rhs.m() || lhs.n() != rhs.n())
            return false;

        for (size_t i = 0; i < rhs.n(); i++)
            for (size_t j = 0; j < rhs.m(); j++)
                if (lhs[i][j] != rhs[i][j])
                    return false;

        return true;
    }

    friend bool operator!=(matrix& lhs, matrix& rhs)
    {
        return !(lhs == rhs);
    }

    matrix& operator+(matrix& obj)
    {
        try
        {

            if (this->m() != obj.m() || this->n() != obj.n())
                throw std::exception("Matrixes spaces are not equal");

            const size_t n = this->n();
            const size_t m = this->m();

            for (size_t i = 0; i < n; i++)
                for (size_t j = 0; j < m; j++)
                    this->matrix_[i][j] += obj.matrix_[i][j];

        } catch (std::exception& e)
        {
            //OutputDebugStringA(e.what());
        }

        return *this;
    }

    matrix& operator-(matrix& obj)
    {
        return obj * -1 + *this;
    }

    matrix& operator*(const int& k)
    {
        for (auto& row : matrix_)
            for (auto& element : row)
                element *= static_cast<T>(k);
        return *this;
    }

    matrix& operator*(const double& k)
    {
        for (auto& row : matrix_)
            for (auto& element : row)
                element *= static_cast<T>(k);
        return *this;
    }

    matrix& operator/(const int& k)
    {
        for (auto& row : matrix_)
            for (auto& element : row)
                element /= static_cast<T>(k);
        return *this;
    }

    matrix& operator/(const double& k)
    {
        for (auto& row : matrix_)
            for (auto& element : row)
                element /= static_cast<T>(k);
        return *this;
    }

    matrix& operator*(matrix& obj)
    {
        auto temp = obj.transpose();

        //obj - 3xN
        //this affine matrix - 3x3
        auto c = new matrix<T>(this->n(), temp.m());
        try
        {
            if (this->m() != temp.n())
                throw std::exception("Number of columns of first matrix is not equal to number of rows of second matrix\nOutputing null matrix");

            /*for (size_t i = 0; i < n(); i++)
                for (size_t j = 0; j < obj.n(); j++)
                    (*c)[i][j] = prod_of_sum(get_column(obj, i), matrix_[j]);*/

            for (size_t i = 0; i < c->n(); i++)
                for (size_t j = 0; j < c->m(); j++)
                    (*c)[i][j] = prod_of_sum((*this)/*.transpose()*/[i], get_column(temp, j));

        } catch(std::exception& e)
        {
                //OutputDebugStringA(e.what());
        }

        return c->transpose();
    }

    std::vector<T>& operator[](const size_t& i)
    {
        return
            matrix_[i];
    }

    friend std::ostream& operator<<(std::ostream& os, matrix& obj)
    {
        const size_t n = obj.n();
        const size_t m = obj.m();

        for (size_t i = 0; i < n; i++)
        {
            for (size_t j = 0; j < m; j++)
            {
                os << obj[i][j] << "\t";
            }
            os << "\n";
        }

        return os;

    }

private:
    static std::vector<std::vector<T>> get_matrix_without_row_column(
        matrix obj, const size_t row, const size_t column
    )
    {
        size_t n = obj.n() - 1;
        size_t m = obj.m() - 1;

        std::vector<std::vector<T>> new_matrix(n);
        for (size_t i = 0; i < n; i++)
            new_matrix[i].resize(m);

        size_t offset_row = 0;
        size_t offset_column = 0;

        for (size_t i = 0; i < n; i++)
        {
            if(i == row)
            {
                offset_row = 1;
            }

            for (size_t j = 0; j < m; j++)
            {

                if (j == column)
                    offset_column = 1;

                new_matrix[i][j] = obj[i + offset_row][j + offset_column];

            }
        }

        return new_matrix;
    }
};

#endif