Matrix: Determinant (2x2)

How to find the determinant of a matrix (2x2): formula, 1 example, and its solution.

Formula

Formula

For a 2x2 square matrix A = [a b / c d],
the determinant, det (A), is
det (A) = ad - bc.

The determinant is written as
det (A), det A, |A|.

The determinant is used
to find the inverse matrix.

Example

Example

Solution

The determinant, det (A),
is equal to,
ad, 1⋅4

minus,
bc, 2⋅3.

So
det (A) = 1⋅4 - 2⋅3.

1⋅4 = 4
-2⋅3 = -6

4 - 6 = -2

So det (A) = -2.