Algebra Examples

$[\begin{array}{c} a & b \\ b & a \end{array}]$

Step 1

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

$a \cdot a - b \cdot b$

Step 2

Simplify each term.

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Step 2.1

Multiply $a$ by $a$ .

$a^{2} - b \cdot b$

Step 2.2

Multiply $b$ by $b$ by adding the exponents.

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Step 2.2.1

Move $b$ .

$a^{2} - (b \cdot b)$

Step 2.2.2

Multiply $b$ by $b$ .

$a^{2} - b^{2}$