Question

Find $AB,$ if $A=\left[\begin{array}{cc}6& 9\\ 2& 3\end{array}\right]$ and $B=\left[\begin{array}{ccc}2& 6& 0\\ 7& 9& 8\end{array}\right]$.

Answer 1

Given: $A=\left[\begin{array}{cc}6& 9\\ 2& 3\end{array}\right]$ and $B=\left[\begin{array}{ccc}2& 6& 0\\ 7& 9& 8\end{array}\right]$
Now,
$AB=\left[\begin{array}{cc}6& 9\\ 2& 3\end{array}\right]\left[\begin{array}{ccc}2& 6& 0\\ 7& 9& 8\end{array}\right]$
$=\left[\begin{array}{ccc}6\left(2\right)+9\left(7\right)& 6\left(6\right)+9\left(9\right)& 6\left(0\right)+9\left(8\right)\\ 2\left(2\right)+3\left(7\right)& 2\left(6\right)+3\left(9\right)& 2\left(0\right)+3\left(8\right)\end{array}\right]$
$=\left[\begin{array}{ccc}12+63& 36+81& 0+72\\ 4+21& 12+27& 0+24\end{array}\right]$
$=\left[\begin{array}{ccc}75& 117& 72\\ 25& 39& 24\end{array}\right]$
Hence, $AB=\left[\begin{array}{ccc}75& 117& 72\\ 25& 39& 24\end{array}\right]$