Question

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

$\left[\begin{array}{cc}17& 0\\ 4& -2\end{array}\right]$

Explanation for the correct option:

Find the value of $AB$:

Given, $A=\left[\begin{array}{ccc}2& 1& 3\\ 4& 1& 0\end{array}\right],B=\left[\begin{array}{cc}1& -1\\ 0& 2\\ 5& 0\end{array}\right]$

$AB=\left[\begin{array}{ccc}2& 1& 3\\ 4& 1& 0\end{array}\right]\left[\begin{array}{cc}1& -1\\ 0& 2\\ 5& 0\end{array}\right]$

$=\left[\begin{array}{cc}2\times 1+1\times 0+3\times 5& 2\times -1+1\times 2+3\times 0\\ 4\times 1+1\times 0+0\times 5& 4\times -1+1\times 2+0\times 0\end{array}\right]$

$\mathbf{\therefore }AB=\left[\begin{array}{cc}17& 0\\ 4& -2\end{array}\right]$

Hence, Option ‘A’ is Correct.