Question

Find $AB,$ if $A=\left[\begin{array}{cc}0& -1\\ 0& 2\end{array}\right]$ and $B=\left[\begin{array}{cc}3& 5\\ 0& 0\end{array}\right]$

Answer 1

Given: $A=\left[\begin{array}{cc}0& -1\\ 0& 2\end{array}\right]$ and $B=\left[\begin{array}{cc}3& 5\\ 0& 0\end{array}\right]$
Now,
$AB={\left[\begin{array}{cc}0& -1\\ 0& 2\end{array}\right]}_{2\times 2}{\left[\begin{array}{cc}3& 5\\ 0& 0\end{array}\right]}_{2\times 2}$
$={\left[\begin{array}{cc}0\times 3+(-1)\times 0& 0\times 5+(-1)\times 0\\ 0\times 3+2\times 0& 0\times 5+2\times 0\end{array}\right]}_{2\times 2}$
$=\left[\begin{array}{cc}0+0& 0+0\\ 0+0& 0+0\end{array}\right]$
$=\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right]$