from copy import deepcopy

class MatrixError(BaseException):
    def __init__(self, m1, m2):
        self.matrix1 = m1
        self.matrix2 = m2


class Matrix:
    def __init__(self, x):
        self.x = deepcopy(x)
    
    def __str__(self):
        res = ''
        for i in range(len(self.x)):
            for j in range(len(self.x[i])):
                res += str(self.x[i][j])
                if j != len(self.x[i]) - 1:
                    res += '\t'
            if i != len(self.x) - 1:
                res += '\n'
        return res

    #size of the matrix
    def size(self):
        return len(self.x), len(self.x[0])

    #Addition
    def __add__(self, m2):
        if self.size() != m2.size():
            raise MatrixError(self, m2)
        else:
            res = Matrix(self.x).x
            for i in range(len(m2.x)):
                for j in range(len(m2.x[0])):
                    res[i][j] += m2.x[i][j]
            return Matrix(res)

    #Multiplication
    def __mul__(self, a):
        if type(a) is not int and type(a) is not float:
            if self.size()[1] != a.size()[0]:
                raise MatrixError(self, a)
            else:
                res = []
                i = 0
                while i < self.size()[0]:
                    tmp = []
                    for j in range(a.size()[1]):
                        cur = 0
                        for k in range(a.size()[0]):
                            cur += self.x[i][k] * a.x[k][j]
                        tmp.append(cur)
                    i += 1
                    res.append(tmp)
                return Matrix(res)
        else:
            res = Matrix(self.x).x
            for i in range(len(res)):
                for j in range(len(res[i])):
                    res[i][j] *= a
            
            return Matrix(res)

    __rmul__ = __mul__

    #Transposition
    def transpose(self):
        res = []
        for j in range(self.size()[1]):
            tmp = []
            for i in range(self.size()[0]):
                tmp.append(self.x[i][j])
            res.append(tmp)
        self.x = res
        return Matrix(res)

    @staticmethod
    def transposed(m):
        res = []
        for j in range(m.size()[1]):
            tmp = []
            for i in range(m.size()[0]):
                tmp.append(m.x[i][j])
            res.append(tmp)
        return Matrix(res)

#Example
m = Matrix([[1, 0, 0],[0, 1, 0],[0, 0, 1]])
m1 = Matrix([[3, 2], [-10, 0], [14, 5]])
m2 = Matrix([[5, 2, 10], [-0.5, -0.25, 18], [-22, -2.5, -0.125]])
m3 = Matrix.transposed(m)
print(5 * m2)
print(m2 * (120 * m * m1))
print(m3)