Question

If the matrices $A = \begin{bmatrix}2&1&3\\ 4&1&0\end{bmatrix}$ and $B = \begin{bmatrix}1&-1\\ 0&2\\ 5&0\end{bmatrix}$, then $AB$ will be

• A. $ \begin{bmatrix}17&0\\ 4&-2\end{bmatrix}$
• B. $ \begin{bmatrix}4&0\\ 0&4\end{bmatrix}$
• C. $ \begin{bmatrix}17&4\\ 0&-2\end{bmatrix}$
• D. $ \begin{bmatrix}0&0\\ 0&0\end{bmatrix}$

Answer 1

Answer: (A)

Given, $A=\begin{bmatrix}2 & 1 & 3 \\ 4 & 1 & 0\end{bmatrix}$ and $B=\begin{bmatrix}1 & -1 \\ 0 & 2 \\ 5 & 0\end{bmatrix}$
Now, $A B=\begin{bmatrix}2 \times 1+1 \times 0+3 \times 5 & 2 \times(-1)+1 \times 2+3 \times 0 \\ 4 \times 1+1 \times 0+0 \times 5 & 4 \times(-1)+1 \times 2+0 \times 0\end{bmatrix}$
$=\begin{bmatrix}17 & 0 \\ 4 & -2\end{bmatrix}$