Algebra Examples

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

Multiply each row in the first matrix by each column in the second matrix.

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

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

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

The matrix is in the most simplified form.

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