Question

If $X=\left[\begin{array}{cc}3& 1\\ -4& -1\end{array}\right],B=\left[\begin{array}{cc}5& 2\\ -2& 1\end{array}\right]$ and $A=\left[\begin{array}{cc}p& q\\ r& s\end{array}\right]$ satisfy the equation $AX=B$, then the matrix $A$ is equal to-

• A. $\left[\begin{array}{cc}-7& 26\\ 1& -5\end{array}\right]$
• B. $\left[\begin{array}{cc}7& 26\\ 4& 17\end{array}\right]$
• C. $\left[\begin{array}{cc}-7& -4\\ 26& 13\end{array}\right]$
• D. $\left[\begin{array}{cc}-7& 26\\ -6& 23\end{array}\right]$

Answer 1

The correct option is A $\left[\begin{array}{cc}-7& 26\\ 1& -5\end{array}\right]$

$AX=B$

$\Rightarrow A=B{X}^{-1}$

$X=\left[\begin{array}{cc}3& 1\\ -4& -1\end{array}\right]⟹X^{-1}=\frac{1}{-3+4}\left[\begin{array}{cc}-1& 4\\ -1& 3\end{array}\right]⟹X^{-1}=\left[\begin{array}{cc}-1& 4\\ -1& 3\end{array}\right]$

$A=B{X}^{-1}⟹\left[\begin{array}{cc}p& q\\ r& s\end{array}\right]=\left[\begin{array}{cc}5& 2\\ -2& 1\end{array}\right]\left[\begin{array}{cc}-1& 4\\ -1& 3\end{array}\right]⟹\left[\begin{array}{cc}p& q\\ r& s\end{array}\right]=\left[\begin{array}{cc}-5-2& 20+6\\ 2-1& -8+3\end{array}\right]⟹\left[\begin{array}{cc}p& q\\ r& s\end{array}\right]=\left[\begin{array}{cc}-7& 26\\ 1& -5\end{array}\right]=A$