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Calculus, Matrices & Vectors · SS 3

Inverse of a 2 × 2 matrix

Undo a matrix, e.g. to solve simultaneous equations.

  • A−1 = 1ad − bc d−b−ca

What the letters mean

a, b, c, d
the entries of A = abcd

Worked example

Find the inverse of 4726.

  1. Step 1: Determinant

    4 × 6 − 7 × 2 = 10

  2. Step 2: Swap a and d, change the signs of b and c

    110 6−7−24 = 0.6−0.7−0.20.4

Final answer: 0.6−0.7−0.20.4

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