📐 Matrix Calculator

2×2 Matrix Operations

A 2×2 matrix has two rows and two columns. Matrix addition and subtraction are element-wise operations. Matrix multiplication follows the row-by-column rule. The determinant of a 2×2 matrix [[a,b],[c,d]] is ad − bc.

Matrix Inverse

The inverse of a 2×2 matrix exists only when the determinant is non-zero. For [[a,b],[c,d]], the inverse is (1/det) × [[d,−b],[−c,a]]. Matrix inverses are used to solve systems of linear equations and in computer graphics transformations.