\documentclass[a4paper, 12 pt]{article}
\pagestyle{empty}
\usepackage[cp1250]{inputenc}
\usepackage{polski}
\usepackage{graphicx}
\usepackage[table]{xcolor}
\usepackage{float}
\usepackage{amsmath}
\usepackage{mathtools}
\begin{document}
\begin{equation}
\delta(i,j) = \begin{cases}
1, & \text{gdy } i = j, \\
0, & \text{gdy } i \neq j, \\
\end{cases}
\end{equation}
\begin{equation}
\det =
 \begin{pmatrix}
  a & b\\
  c & d\\
 \end{pmatrix} = ad - bc
\end{equation}

\begin{equation}
 \begin{bmatrix}
  a_{11} & a_{12}\\
  a_{21} & a_{22}\\
 \end{bmatrix}
 \begin{bmatrix}
  b_{11} & b_{12}\\
  b_{21} & b_{22}\\
 \end{bmatrix} =
\begin{bmatrix}
  b_{11} + a_{11} & b_{11} + a_{11}\\
  b_{11} + a_{11} & b_{11} + a_{11}\\
 \end{bmatrix}

\end{equation}

\end{document}