Linear Algebra Examples

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

Step 1

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

$1 \cdot 1 - a \cdot a$

Step 2

Simplify each term.

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Step 2.1

Multiply $1$ by $1$ .

$1 - a \cdot a$

Step 2.2

Multiply $a$ by $a$ by adding the exponents.

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Step 2.2.1

Move $a$ .

$1 - (a \cdot a)$

Step 2.2.2

Multiply $a$ by $a$ .

$1 - a^{2}$