Back to Vectors, Matrices and Conics
Determinant and inverse of a 2 × 2 matrix
Questions at easy, medium and hard levels. Pick a level and get a fresh set every time, with instant feedback.
Learn it For A = [a b; c d], det A = ad − bc. If det A ≠ 0, A⁻¹ = (1/det A)[d −b; −c a]. Inverses solve matrix equations: AX = B gives X = A⁻¹B.
Example: Solve 2x + y = 7, x + 3y = 11 with matrices.
- det = 6 − 1 = 5. A⁻¹ = (1/5)[3 −1; −1 2].
- X = A⁻¹[7; 11] = (1/5)[10; 15] = (2, 3).
Loading questions…