Precalculus Examples

$[\begin{array}{c} - 2 & 6 \\ - 1 & 3 \end{array}]$

Step 1

Find the determinant.

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Step 1.1

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$- 2 \cdot 3 - (- 1 \cdot 6)$

Step 1.2

Simplify the determinant.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Multiply $- 2$ by $3$ .

$- 6 - (- 1 \cdot 6)$

Step 1.2.1.2

Multiply $- (- 1 \cdot 6)$ .

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Step 1.2.1.2.1

Multiply $- 1$ by $6$ .

$- 6 - - 6$

Step 1.2.1.2.2

Multiply $- 1$ by $- 6$ .

$- 6 + 6$

Step 1.2.2

Add $- 6$ and $6$ .

$0$

Step 2

There is no inverse because the determinant is $0$ .