Question

If $A=\left[\begin{array}{cc}1& -1\\ 2& -1\end{array}\right]$ , $B=\left[\begin{array}{cc}2& 1\\ 1& -1\end{array}\right]$, find $AB$.

Answer 1

$A=\left[\begin{array}{cc}1& -1\\ 2& -1\end{array}\right]$ and $B=\left[\begin{array}{cc}2& 1\\ 1& -1\end{array}\right]$

$AB=\left[\begin{array}{cc}1& -1\\ 2& -1\end{array}\right]\left[\begin{array}{cc}2& 1\\ 1& -1\end{array}\right]$

$AB=\left[\begin{array}{cc}2-1& 1+1\\ 4-1& 2+1\end{array}\right]=\left[\begin{array}{cc}1& 2\\ 3& 3\end{array}\right]$