Examples

[\begin{matrix} 1 & 2 2 & 1 \end{matrix}]

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

Step 1

The determinant of a

2 \times 2

$2 \times 2$ matrix can be found using the formula

∣ ∣ ∣ \begin{matrix} a & b c & d \end{matrix} ∣ ∣ ∣ = a d - c b

$| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

1 \cdot 1 - 2 \cdot 2

$1 \cdot 1 - 2 \cdot 2$

Step 2

Simplify the determinant.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply

1

$1$ by

1

$1$ .

1 - 2 \cdot 2

$1 - 2 \cdot 2$

Step 2.1.2

Multiply

- 2

$- 2$ by

2

$2$ .

1 - 4

$1 - 4$

1 - 4

$1 - 4$

Step 2.2

Subtract

4

$4$ from

1

$1$ .

- 3

$- 3$

- 3

$- 3$

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