Question

If $A=\left[\begin{array}{ccc}1& -2& 3\\ -4& 2& 5\end{array}\right]$ and $B=\left[\begin{array}{cc}2& 3\\ 4& 5\\ 2& 1\end{array}\right]$, then find $AB$

Answer 1

We have,

$A=\left[\begin{array}{ccc}1& -2& 3\\ -4& 2& 5\end{array}\right]$ and $B=\left[\begin{array}{cc}2& 3\\ 4& 5\\ 2& 1\end{array}\right]$

Now,

$AB=\left[\begin{array}{ccc}1& -2& 3\\ -4& 2& 5\end{array}\right]\left[\begin{array}{cc}2& 3\\ 4& 5\\ 2& 1\end{array}\right]$

$AB=\left[\begin{array}{cc}2-8+6& 3-10+3\\ -8+8+10& -12+10+5\end{array}\right]$

$AB=\left[\begin{array}{cc}0& -4\\ 10& 3\end{array}\right]$

Hence, this is the answer.