2x2 Matrix Calculator

For a 2×2 matrix [a b; c d], the determinant is ad − bc. The matrix [3 8; 4 6] has determinant 3 × 6 − 8 × 4 = 18 − 32 = −14. A matrix has an inverse only when its determinant is not zero. The inverse is (1 ÷ det) × [d −b; −c a], so for [2 1; 1 1] the determinant is 2 − 1 = 1 and the inverse is [1 −1; −1 2]. A zero determinant means the rows are proportional and the matrix is singular, which for a pair of linear equations means they have no unique solution. Determinants and inverses are used to solve simultaneous equations and describe geometric transformations.