Multiply the Matrices [[0,0,1],[1,0,0],[0,1,0]][[0,0,1],[0,1,0],[1,0,0]]

$[\begin{array}{c} 0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \end{array}] [\begin{array}{c} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array}]$

Multiply each row in the first matrix $[\begin{array}{c} 0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \end{array}]$ by each column in the second matrix $[\begin{array}{c} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array}]$ .

$[\begin{array}{c} 0 \cdot 0 + 0 \cdot 0 + 1 \cdot 1 & 0 \cdot 0 + 0 \cdot 1 + 1 \cdot 0 & 0 \cdot 1 + 0 \cdot 0 + 1 \cdot 0 \\ 1 \cdot 0 + 0 \cdot 0 + 0 \cdot 1 & 1 \cdot 0 + 0 \cdot 1 + 0 \cdot 0 & 1 \cdot 1 + 0 \cdot 0 + 0 \cdot 0 \\ 0 \cdot 0 + 1 \cdot 0 + 0 \cdot 1 & 0 \cdot 0 + 1 \cdot 1 + 0 \cdot 0 & 0 \cdot 1 + 1 \cdot 0 + 0 \cdot 0 \end{array}]$

Simplify each element of the matrix by multiplying out all the expressions.

$[\begin{array}{c} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{array}]$

$[\begin{array}{c} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{array}]$ is in the most simplified form.

$[\begin{array}{c} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{array}]$

Multiply the Matrices [[0,0,1],[1,0,0],[0,1,0]][[0,0,1],[0,1,0],[1,0,0]]

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