Question

 If \[A = \begin{bmatrix}2 & 4 & - 1 \\ - 1 & 0 & 2\end{bmatrix}, B = \begin{bmatrix}3 & 4 \\ - 1 & 2 \\ 2 & 1\end{bmatrix}\],find `(AB)^T`

 

Answer 1

\[Here, \] 

\[AB = \begin{bmatrix}2 & 4 & - 1 \\ - 1 & 0 & 2\end{bmatrix}\begin{bmatrix}3 & 4 \\ - 1 & 2 \\ 2 & 1\end{bmatrix}\] 

\[ \Rightarrow AB = \begin{bmatrix}6 - 4 - 2 & 8 + 8 - 1 \\ - 3 - 0 + 4 & - 4 + 0 + 2\end{bmatrix}\] 

\[ \Rightarrow AB = \begin{bmatrix}0 & 15 \\ 1 & - 2\end{bmatrix}\] 

\[ \Rightarrow \left( AB \right)^T = \begin{bmatrix}0 & 1 \\ 15 & - 2\end{bmatrix}\]