1.4.21 Matrix transformations

condition: Given a matrix \( M=\left(\begin{array}{ccc}-2 & -1 & 4 \\ 0 & 0 & 2 \\ 1 & 1 & -1\end{array}\right) \) : a) find the minor and algebraic complement of the element \( m_{23} \) matrices \( M \); b) calculate the determinant of the matrix \( M \) using the 2nd row expansion method; c) show that the matrix \( M \) is invertible and find the matrix inverse to the matrix \( M\left(M^{-1}\right) \), do a check (i.e. show that \( M M^{-1}=E \) ).