Examples

$[\begin{array}{c} 1 & 0 \\ 0 & 1 \end{array}] + [\begin{array}{c} - 1 & - 1 \\ 2 & - 2 \end{array}]$

Step 1

Add the corresponding elements.

$[\begin{array}{c} 1 - 1 & 0 - 1 \\ 0 + 2 & 1 - 2 \end{array}]$

Step 2

Simplify each element.

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Step 2.1

Subtract $1$ from $1$ .

$[\begin{array}{c} 0 & 0 - 1 \\ 0 + 2 & 1 - 2 \end{array}]$

Step 2.2

Subtract $1$ from $0$ .

$[\begin{array}{c} 0 & - 1 \\ 0 + 2 & 1 - 2 \end{array}]$

Step 2.3

Add $0$ and $2$ .

$[\begin{array}{c} 0 & - 1 \\ 2 & 1 - 2 \end{array}]$

Step 2.4

Subtract $2$ from $1$ .

$[\begin{array}{c} 0 & - 1 \\ 2 & - 1 \end{array}]$

Step 3

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

$0 \cdot - 1 - 2 \cdot - 1$

Step 4

Simplify the determinant.

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply $0$ by $- 1$ .

$0 - 2 \cdot - 1$

Step 4.1.2

Multiply $- 2$ by $- 1$ .

$0 + 2$

Step 4.2

Add $0$ and $2$ .

$2$

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