Question

If $A=\left[\begin{array}{ccc}2& 0& 0\\ 0& 2& 0\\ 0& 0& 2\end{array}\right]$, then value of $A^{-1}$ is

• A. $\left[\begin{array}{ccc}1& 0& 1\\ 0& 1& 1\\ 0& 0& 1\end{array}\right]$
• B. $\left[\begin{array}{ccc}\frac{1}{2}& 0& 0\\ 0& \frac{1}{2}& 0\\ 0& 0& \frac{1}{2}\end{array}\right]$
• C. $\left[\begin{array}{ccc}2& 0& 0\\ 0& -2& 0\\ 0& 0& -2\end{array}\right]$
• D. None of these

Answer 1

Answer: (B)

$\left[\begin{array}{ccc}\frac{1}{2}& 0& 0\\ 0& \frac{1}{2}& 0\\ 0& 0& \frac{1}{2}\end{array}\right]$

$A=\left[\begin{array}{ccc}2& 0& 0\\ 0& 2& 0\\ 0& 0& 2\end{array}\right]=2\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]=2I$
$\Rightarrow A{A}^{-1}=2I{A}^{-1}$
$\Rightarrow I=2A^{-1}$
$\Rightarrow A^{-1}=\left[\begin{array}{ccc}\frac{1}{2}& 0& 0\\ 0& \frac{1}{2}& 0\\ 0& 0& \frac{1}{2}\end{array}\right]$
Ans: B