Question

$\text{If}A=\left[\begin{array}{cc}5& 0\\ 2& 2\end{array}\right],\text{then find}A\times I_{2\times 2}.$

• A. $$\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right]$$
• B. $$\left[\begin{array}{cc}5& 0\\ 2& 2\end{array}\right]$$
• C. $$\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$$
• D. $$\left[\begin{array}{cc}-5& 0\\ -2& -2\end{array}\right]$$

Answer 1

The correct option is B $$\left[\begin{array}{cc}5& 0\\ 2& 2\end{array}\right]$$

We know from properties that, if $A$ is a square matrix of order $n\times n$ and $I$ is the unit matrix of the same order, then
$A\times I=I\times A=A\therefore A\times I_{2\times 2}=\left[\begin{array}{cc}5& 0\\ 2& 2\end{array}\right]$