Question

If $A=\left[\begin{array}{cc}2& 3\\ 2& -1\end{array}\right]$, then find $8A^{-1}$.

• A. $\left[\begin{array}{cc}1& 3\\ 2& -2\end{array}\right]$
• B. $\left[\begin{array}{cc}1& 3\\ -2& 2\end{array}\right]$
• C. $\left[\begin{array}{cc}-1& 3\\ 2& 2\end{array}\right]$
• D. $\left[\begin{array}{cc}1& 2\\ 3& -2\end{array}\right]$
• E. None of these

Answer 1

The correct option is A $\left[\begin{array}{cc}1& 3\\ 2& -2\end{array}\right]$

Given, $A=\left[\begin{array}{cc}2& 3\\ 2& -1\end{array}\right]$
$|A|=-2-6=-8$, so we can find its inverse.
Now, $adjA=\left[\begin{array}{cc}-1& -3\\ -2& 2\end{array}\right]$
So, $A^{-1}=\frac{1}{-8}\left[\begin{array}{cc}-1& -3\\ -2& 2\end{array}\right]$
$\Rightarrow 8A^{-1}=\left[\begin{array}{cc}1& 3\\ 2& -2\end{array}\right]$