Question

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

• A. $-A$
• B. $A$
• C. $1$
• D. None of these

Answer 1

The correct option is B $A$

We have, $A=\left[\begin{array}{ccc}0& 0& 1\\ 0& 1& 0\\ 1& 0& 0\end{array}\right]$
$\Rightarrow |A|=0(0-0)-0(0-0)+1(0-1)$
$\Rightarrow |A|=-1$
and cofactors of A are
$A_{11}=0,A_{12}=0,A_{13}=-1,$
$A_{21}=0,A_{22}=-1,A_{23}=0,$
$A_{31}=-1,A_{32}=0,A_{33}=0$
$\therefore A^{-1}=\frac{adj\left(A\right)}{|A|}$
$=-\frac{1}{1}\left[\begin{array}{ccc}0& 0& -1\\ 0& -1& 0\\ -1& 0& 0\end{array}\right]$