Question

If $A=\left[\begin{array}{cc}2& 2\\ 9& 4\end{array}\right]$ and $I=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$, then $10A^{-1}$ is equal to:

• A. $6I-A$
• B. $A-6I$
• C. $4I-A$
• D. $A-4I$

Answer 1

The correct option is B $A-6I$

$A=\left[\begin{array}{cc}2& 2\\ 9& 4\end{array}\right]$

$A^{-1}=-\frac{1}{10}\left[\begin{array}{cc}4& -2\\ -9& 2\end{array}\right]$

$\Rightarrow 10A^{-1}=\left[\begin{array}{cc}-4& 2\\ 9& -2\end{array}\right]\Rightarrow 10A^{-1}=A-6I$