Given the matrix A :
[tex]A=\begin{bmatrix}{0} & {0} & {1} \\ {1} & {0} & {0} \\ {0} & {1} & {0}\end{bmatrix}[/tex]
The determinant of the matrix will be =
[tex]1\cdot(1\cdot1-0)=1[/tex]
Now, we will find the transpose of the matrix :
[tex]A^T=\begin{bmatrix}{0} & {1} & {0} \\ {0} & {0} & {1} \\ {1} & {0} & {0}\end{bmatrix}[/tex]
Then, find the elements of the inverse :
[tex]\text{adj(A)}=\begin{bmatrix}{0} & {1} & {0} \\ {0} & {0} & {1} \\ {1} & {0} & {0}\end{bmatrix}[/tex]
So, the inverse will be :
[tex]A^{-1}=\frac{adj(A)}{\det (A)}=\begin{bmatrix}{0} & {1} & {0} \\ {0} & {0} & {1} \\ {1} & {0} & {0}\end{bmatrix}[/tex]
