Question

If $X$ and $Y$ are $2\times 2$ matrices such that $2X+3Y=O$ and $X+2Y=I,$ where $O$ and $I$ denote the $2\times 2$ zero matrix and the $2\times 2$ identity matrix, then $X$ is equal to

• A. $\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$
• B. $\left[\begin{array}{cc}2& 0\\ 0& 2\end{array}\right]$
• C. $\left[\begin{array}{cc}-3& 0\\ 0& -3\end{array}\right]$
• D. $\left[\begin{array}{cc}3& 0\\ 0& 3\end{array}\right]$

Answer 1

Answer: (C)

Given, $2X+3Y=O$ .....(i) and $X+2Y=I$ ..(ii)
Where $O=\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right]$ and $I=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$
On solving Eqs. (i) and (ii), we get
$X=-3I=\left[\begin{array}{cc}-3& 0\\ 0& -3\end{array}\right]$