# Determinant of a Matrix (2x2)

How to find the determinant of a matrix (2x2): formula, examples, and their solutions.

## Formula

For a 2×2 matrix [*a* *b* / *c* *d*],

the determinant of the matrix is

|*a* *b* / *c* *d*| = *ad* - *bc*.

It determines the properties of a matrix.

One of the properties

that the determinant of a matrix determines

is to see if the matrix has an inverse matrix.

## Example 1

|1 2 / 3 4| = 1⋅4 - 2⋅3 = -2.

## Example 2

det[2 7 / 3 *x*] is another way

to write the determinant of [2 7 / 3 *x*].

So |2 7 / 3 *x*| = 2*x* - 7⋅3.

It says det[2 7 / 3 *x*] = 5.

So |2 7 / 3 *x*| = 2*x* - 7⋅3 = 2*x* - 21 = 5.