Question

If $A=\begin{bmatrix}1 & -2 & 1 \\ 2 & 1 & 3\end{bmatrix}B=\begin{bmatrix}2 & 1 \\ 3 & 2 \\ 1 & 1\end{bmatrix}$ then $(A B)'$ is equal to

• A. $\begin{bmatrix}-3 & -2 \\ 10 & 7\end{bmatrix}$
• B. $\begin{bmatrix}-3 & 10 \\ -2 & 7\end{bmatrix}$
• C. $\begin{bmatrix}-3 & 7 \\ 10 & 2\end{bmatrix}$
• D. $\begin{bmatrix}-3 & 7 \\ 10 & -2\end{bmatrix}$

Answer 1

Answer: (B)

$A B=\begin{pmatrix}-3 & -2 \\ 10 & 7\end{pmatrix}$
$(A B)^{T}=\begin{pmatrix}-3 & 10 \\ -2 & 7\end{pmatrix}$