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# The inverse of the matrix $\begin{bmatrix} 0 & 0 & 1 \\0 & 1 & 0 \\1 & 0 & 0 \end{bmatrix}$ is

$\begin{array} {1 1}(1)\begin{bmatrix} 1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1 \end{bmatrix}&(2)\begin{bmatrix} 0 & 0 & 1 \\0 & 1 & 0 \\-1 & 0 & 0 \end{bmatrix}\\(3)\begin{bmatrix} 0 & 0 & 1 \\0 & 1 & 0 \\1 & 0 & 0 \end{bmatrix}&(4)\begin{bmatrix} -1 & 0 & 0 \\0 & -1 & 0 \\0 & 0 & 1 \end{bmatrix}\end{array}$

Can you answer this question?

$A= \begin{bmatrix} 0 & 0 & 1 \\0 & 1 & 0 \\1 & 0 & 0 \end{bmatrix}$
$|A|=0+0-1=-1$
co factor matrix of $A =\begin{bmatrix} 0 & 0 & 1 \\0 & -1 & 0 \\-1 & 0 & 0 \end{bmatrix}$
$adj A =\begin{bmatrix} 0 & 0 & -1 \\0 & -1 & 0 \\-1 & 0 & 0 \end{bmatrix}$
$A^{-1}=\large\frac{1}{-1} \begin{bmatrix} 0 & 0 & -1 \\0 & -1 & 0 \\-1 & 0 & 0 \end{bmatrix}$
$\qquad=\begin{bmatrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\1 & 0 & 0 \end{bmatrix}$
Hence 3 is the correct answer.
answered May 2, 2014 by