Question

If $A$ be a matrix such that, inverse of $7A$ is the matrix $\left[\begin{array}{cc}-1& 2\\ 4& -7\end{array}\right]$, then $A$ equals

• A. $\left[\begin{array}{cc}1& 2\\ 4& 1\end{array}\right]$
• B. $\left[\begin{array}{cc}1& 4/7\\ 2/7& 1/7\end{array}\right]$
• C. $\left[\begin{array}{cc}1& 4\\ 2& 1\end{array}\right]$
• D. $\left[\begin{array}{cc}1& 2/7\\ 4/7& 1/7\end{array}\right]$

Answer 1

The correct option is D $\left[\begin{array}{cc}1& 2/7\\ 4/7& 1/7\end{array}\right]$

${\left(7A\right)}^{-1}=\left[\begin{array}{cc}-1& 2\\ 4& -7\end{array}\right]$

$\Rightarrow {\left({\left(7A\right)}^{-1}\right)}^{-1}={\left[\begin{array}{cc}-1& 2\\ 4& -7\end{array}\right]}^{-1}$

$\Rightarrow 7A=\frac{-1}{1}\left[\begin{array}{cc}-7& -2\\ -4& -1\end{array}\right]$

$\Rightarrow A=\frac{1}{7}\left[\begin{array}{cc}7& 2\\ 4& 1\end{array}\right]$

$\Rightarrow A=\left[\begin{array}{cc}1& \frac{2}{7}\\ \frac{4}{7}& \frac{1}{7}\end{array}\right]$
Ans: D