Question

The inverse of Matrix $A=\left[\begin{array}{ccc}0& 1& 0\\ 1& 0& 0\\ 0& 0& 1\end{array}\right]$ is

• A. $A$
• B. $A^T$
• C. $\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$
• D. $\left[\begin{array}{ccc}1& 0& 0\\ 1& 0& 0\\ 0& 1& 0\end{array}\right]$

Answer 1

The correct option is A $A$

$A=\left[\begin{array}{ccc}0& 1& 0\\ 1& 0& 0\\ 0& 0& 1\end{array}\right]$
Here, $|A|=-1$
Now, $adjA=C^T={\left[\begin{array}{ccc}0& -1& 0\\ -1& 0& 0\\ 0& 0& -1\end{array}\right]}^T$
$\Rightarrow adjA=\left[\begin{array}{ccc}0& -1& 0\\ -1& 0& 0\\ 0& 0& -1\end{array}\right]$
$\Rightarrow A^{-1}=\left[\begin{array}{ccc}0& 1& 0\\ 1& 0& 0\\ 0& 0& 1\end{array}\right]$
$\Rightarrow A^{-1}=A$