Matrix Calculator

Determinant and inverse of a 2×2 matrix.

Matrix Calculator helps you determinant and inverse of a 2×2 matrix. Enter a (top left), b (top right), c (bottom left), and d (bottom right), review the breakdown, and use the guidance below to understand what the number means — and what it does not. What the Matrix calculator does Matrix Calculator is built for arithmetic, algebra, geometry, and number tools. Determinant and inverse of a 2×2 matrix. You enter a (top left), b (top right), c (bottom left), and d (bottom right), then Simple Calculators computes the result instantly. Results use standard school and engineering formulas that run privately in your browser. How the math works Enter the four numbers: a (top left), b (top right), c (bottom left) and d (bottom right). The determinant = a × d − b × c. If it is not 0, the inverse is found by swapping a and d, changing the signs of b and c, and dividing every entry by the determinant. This calculator handles 2×2 matrices only; it also shows the trace (a + d). The formula: det = a × d − b × c; A⁻¹ = (1 ÷ det) × [d, −b; −c, a]. For the matrix [a, b; c, d] (top row a, b; bottom row c, d). There is no inverse when det = 0.