Perform matrix operations on 2×2 or 3×3 matrices
This matrix calculator performs basic linear algebra operations on 2×2 and 3×3 matrices, including addition, subtraction, and multiplication. For 2×2 matrices, it also computes the determinant and inverse, which are fundamental concepts in linear algebra used across engineering and physics.
Matrix addition and subtraction are performed element by element. Matrix multiplication multiplies rows of the first matrix by columns of the second. The determinant of a 2×2 matrix [a b; c d] is ad − bc. The inverse exists only when the determinant is non-zero.
Matrix multiplication is possible only when the number of columns in the first matrix equals the number of rows in the second. For square matrices of the same size (like 2×2 and 2×2), multiplication is always defined, but the result depends on the order (A×B ≠ B×A in general).
A zero determinant means the matrix is singular (non-invertible). This implies that the rows or columns are linearly dependent, meaning the transformation represented by the matrix collapses space into a lower dimension. In practical terms, the system of equations has either no solution or infinitely many.