Question

Let $A=\left[\begin{array}{cc}2& 4\\ 3& 2\end{array}\right],B=\left[\begin{array}{cc}1& 3\\ -2& 5\end{array}\right],$
Find the value of the following:
AB

Answer 1

$AB=\left[\begin{array}{cc}2& 4\\ 3& 2\end{array}\right]\left[\begin{array}{cc}1& 3\\ -2& 5\end{array}\right]=\left[\begin{array}{cc}2\times 1+4\times (-2)& 2\times 3+4\times 5\\ 3\times 1+2\times (-2)& 3\times 3+2\times 5\end{array}\right]=\left[\begin{array}{cc}-6& 26\\ -1& 19\end{array}\right]$

If two matrices have different orders then we can neither add nor subtract the matrices but we can multiply the matrices either the orders are same or number of columns of first matrix is equal to the number of rows of second matrix.