Finite Math Examples

$A B = [\begin{array}{c} 2 & - 3 \\ - 3 & 5 \end{array}] [\begin{array}{c} 5 & 3 \\ 3 & 2 \end{array}]$

Step 1

Assuming that $X$ is the matrix to solve for, multiply the inverse matrix by both sides of the equation.

Step 2

Simplify the right side of the equation.

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

$x = [\begin{array}{c} 2 \cdot 5 - 3 \cdot 3 & 2 \cdot 3 - 3 \cdot 2 \\ - 3 \cdot 5 + 5 \cdot 3 & - 3 \cdot 3 + 5 \cdot 2 \end{array}]$

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

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

The matrix is in the most simplified form.

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