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  4. The inverse of the matrix A =[0 1 0 1 0 0 0 0 1] is

Q. The inverse of the matrix $A =\begin{bmatrix}0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1\end{bmatrix}$ is

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Solution:

$\text{det} A =-1(1-0)=-1 \text{adj} A =\begin{bmatrix}0 & -1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & -1\end{bmatrix} \quad \frac{\text{adj} A}{\text{det} A}=\begin{bmatrix}0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1\end{bmatrix}= A ^{\prime}$

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