Examples

$[\begin{array}{c} 2 & 4 \\ 6 & 8 \end{array}] + [\begin{array}{c} 1 & 2 \\ 3 & 4 \end{array}]$

Step 1

Add the corresponding elements.

$[\begin{array}{c} 2 + 1 & 4 + 2 \\ 6 + 3 & 8 + 4 \end{array}]$

Step 2

Simplify each element.

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Step 2.1

Add $2$ and $1$ .

$[\begin{array}{c} 3 & 4 + 2 \\ 6 + 3 & 8 + 4 \end{array}]$

Step 2.2

Add $4$ and $2$ .

$[\begin{array}{c} 3 & 6 \\ 6 + 3 & 8 + 4 \end{array}]$

Step 2.3

Add $6$ and $3$ .

$[\begin{array}{c} 3 & 6 \\ 9 & 8 + 4 \end{array}]$

Step 2.4

Add $8$ and $4$ .

$[\begin{array}{c} 3 & 6 \\ 9 & 12 \end{array}]$

Step 3

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

$3 \cdot 12 - 9 \cdot 6$

Step 4

Simplify the determinant.

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply $3$ by $12$ .

$36 - 9 \cdot 6$

Step 4.1.2

Multiply $- 9$ by $6$ .

$36 - 54$

Step 4.2

Subtract $54$ from $36$ .

$- 18$

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