Examples

$[\begin{array}{c} - 2 & 0 \\ - 5 & - 4 \end{array}] + [\begin{array}{c} - 4 & 0 \\ 2 & 2 \end{array}]$

Step 1

Add the corresponding elements.

$[\begin{array}{c} - 2 - 4 & 0 + 0 \\ - 5 + 2 & - 4 + 2 \end{array}]$

Step 2

Simplify each element.

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Step 2.1

Subtract $4$ from $- 2$ .

$[\begin{array}{c} - 6 & 0 + 0 \\ - 5 + 2 & - 4 + 2 \end{array}]$

Step 2.2

Add $0$ and $0$ .

$[\begin{array}{c} - 6 & 0 \\ - 5 + 2 & - 4 + 2 \end{array}]$

Step 2.3

Add $- 5$ and $2$ .

$[\begin{array}{c} - 6 & 0 \\ - 3 & - 4 + 2 \end{array}]$

Step 2.4

Add $- 4$ and $2$ .

$[\begin{array}{c} - 6 & 0 \\ - 3 & - 2 \end{array}]$

Step 3

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

$- 6 \cdot - 2 - (- 3 \cdot 0)$

Step 4

Simplify the determinant.

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply $- 6$ by $- 2$ .

$12 - (- 3 \cdot 0)$

Step 4.1.2

Multiply $- (- 3 \cdot 0)$ .

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Step 4.1.2.1

Multiply $- 3$ by $0$ .

$12 - 0$

Step 4.1.2.2

Multiply $- 1$ by $0$ .

$12 + 0$

Step 4.2

Add $12$ and $0$ .

$12$

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