Question:
If $A=\left[\begin{array}{rrr}2 & 4 & -1 \\ -1 & 0 & 2\end{array}\right], B=\left[\begin{array}{rr}3 & 4 \\ -1 & 2 \\ 2 & 1\end{array}\right]$, find $(A B)^{T}$
Solution:
Here,
$A B=\left[\begin{array}{ccc}2 & 4 & -1 \\ -1 & 0 & 2\end{array}\right]\left[\begin{array}{cc}3 & 4 \\ -1 & 2 \\ 2 & 1\end{array}\right]$
$\Rightarrow A B=\left[\begin{array}{cc}6-4-2 & 8+8-1 \\ -3-0+4 & -4+0+2\end{array}\right]$
$\Rightarrow A B=\left[\begin{array}{cc}0 & 15 \\ 1 & -2\end{array}\right]$
$\Rightarrow(A B)^{T}=\left[\begin{array}{cc}0 & 1 \\ 15 & -2\end{array}\right]$