Inverse of a 2×2 matrix
Guided practice — solve each problem, check, then generate a fresh one.
Formula to apply
A⁻¹ = (1/det) [[d, −b], [−c, a]]
Problem
A⁻¹ has integer entries when det = ±1. Find A⁻¹ for
A = [ 2 3 ]
[ 1 2 ]
Enter the four entries as top-left, top-right, bottom-left, bottom-right.
Working
- 1det = a·d − b·c = 2·2 − 3·(1) = 1.
- 2A⁻¹ = (1/1)·[ 2 -3 ; -1 2 ].
- 3Since det = 1: A⁻¹ = [ 2 -3 ; -1 2 ].