Question

If the matrices $A=\left[\begin{array}{ccc}2& 1& 3\\ 4& 1& 0\end{array}\right]$ and $B=\left[\begin{array}{cc}1& -1\\ 0& 2\\ 5& 0\end{array}\right]$, then AB will be

• A. $\left[\begin{array}{cc}17& 0\\ 4& -2\end{array}\right]$
• B. $\left[\begin{array}{cc}4& 0\\ 0& 4\end{array}\right]$
• C. $\left[\begin{array}{cc}17& 4\\ 0& -2\end{array}\right]$
• D. $\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right]$

Answer 1

The correct option is A $\left[\begin{array}{cc}17& 0\\ 4& -2\end{array}\right]$

Given, $A=\left[\begin{array}{ccc}2& 1& 3\\ 4& 1& 0\end{array}\right]$ and $B=\left[\begin{array}{cc}1& -1\\ 0& 2\\ 5& 0\end{array}\right]$
Now, $AB=\left[\begin{array}{cc}2\times 1+1\times 0+3\times 5& 2\times (-1)+1\times 2+3\times 0\\ 4\times 1+1\times 0+0\times 5& 4\times (-1)+1\times 2+0\times 0\end{array}\right]$
$=\left[\begin{array}{cc}17& 0\\ 4& -2\end{array}\right]$