Question

The inverse of the matrix $\left[\begin{array}{ccc}0& 0& 1\\ 0& 1& 0\\ 1& 0& 0\end{array}\right]$ is:

• A. $\left[\begin{array}{ccc}0& 0& 1\\ 0& 1& 0\\ 1& 0& 0\end{array}\right]$
• B. $\left[\begin{array}{ccc}0& 0& -1\\ 0& -1& 0\\ -1& 0& 0\end{array}\right]$
• C. $\left[\begin{array}{ccc}0& 0& -1\\ 0& 1& 1\\ -1& 0& 1\end{array}\right]$
• D. $\left[\begin{array}{ccc}1& 3& 3\\ 1& 4& 3\\ 1& 3& 4\end{array}\right]$

Answer 1

The correct option is A $\left[\begin{array}{ccc}0& 0& 1\\ 0& 1& 0\\ 1& 0& 0\end{array}\right]$

(A) Let
$A=\left[\begin{array}{ccc}0& 0& 1\\ 0& 1& 0\\ 1& 0& 0\end{array}\right]$
$\left|A\right|=1\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]=-1$
$Adj.A=\left[\begin{array}{ccc}0& 0& -1\\ 0& -1& 0\\ -1& 0& 0\end{array}\right]$
$A^{-1}=\frac{1}{\left|A\right|}=\left[\begin{array}{ccc}0& 0& 1\\ 0& 1& 0\\ 1& 0& 0\end{array}\right]=A$