18 min read

The Determinant of a 2×2 Matrix

The determinant is a single number, calculated from a matrix, that reveals important properties about it.

One Number, Many Clues

Matrix lab

Matrix A

Determinant of A: 2.0000

Change entries and watch the determinant update.

Change a value and watch:

Change the matrix entries and watch the determinant update: ad - bc.

The determinant is a single number — it summarises the whole matrix in one value.

Example 1 — a positive determinant

Find the determinant of (3254) . 1 Multiply the main diagonal: 3 \times 4 = 12 2 Multiply the other diagonal: 5 \times 2 = 10 3 Subtract: 12 - 10 Answer: 2

Example 2 — a determinant of zero

Find the determinant of (6321) . 1 Main diagonal: 6 \times 1 = 6 2 Other diagonal: 2 \times 3 = 6 3 Subtract: 6 - 6 Answer: 0 (this matters — the next lesson explains why)

Practice

Find the determinant of (7245) .

Your answer