Question

If $A=\left[\begin{array}{ccc}2& 4& -1\\ -1& 0& 2\end{array}\right],B=\left[\begin{array}{cc}3& 4\\ -1& 2\\ 2& 1\end{array}\right]$, find (AB)^T

Answer 1

$$\begin{gathered} \mathrm{Here}, \\ AB=\left[\begin{array}{ccc}2& 4& -1\\ -1& 0& 2\end{array}\right]\left[\begin{array}{cc}3& 4\\ -1& 2\\ 2& 1\end{array}\right] \\ \Rightarrow AB=\left[\begin{array}{cc}6-4-2& 8+8-1\\ -3-0+4& -4+0+2\end{array}\right] \\ \Rightarrow AB=\left[\begin{array}{cc}0& 15\\ 1& -2\end{array}\right] \\ \Rightarrow {\left(AB\right)}^T=\left[\begin{array}{cc}0& 1\\ 15& -2\end{array}\right] \end{gathered}$$