Calculus, Matrices & Vectors · SS 3
Determinant of a 2 × 2 matrix
Find the determinant, needed for the inverse and for solving equations with matrices.
- For A = abcd, |A| = ad − bc
What the letters mean
- a, b, c, d
- the four entries of the matrix
Worked example
Find the determinant of 3214.
Step 1: Leading diagonal minus the other diagonal
3 × 4 − 2 × 1 = 12 − 2 = 10
Final answer: 10
If the determinant is 0, the matrix has no inverse (it is singular).
See it
Play with this picture from the Determinants lesson.
A =
Selected entry (a)5
unit square (area 1) → parallelogram with sides (a, c) and (b, d)
|A| = ad − bc = 5 × 4 − 2 × 3 = 20 − 6 = 14
Area of the parallelogram = |14| = 14
A−1 = 1 ÷ 14 × 4−2−35