Matrix Calculator

The calculator supports addition, subtraction, scalar multiplication, matrix multiplication, transposition, determinant calculation, inverse (when it exists), trace (sum of diagonal), row echelon form, and rank. Enter matrix values into a grid interface and select the operation you need.

To multiply matrix A (m x n) by matrix B (n x p), each element of the result is the dot product of a row from A and a column from B. The result is an m x p matrix. Matrix A's column count must equal matrix B's row count. The calculator shows each dot product step for educational clarity.

For a 2x2 matrix [[a,b],[c,d]], det = ad - bc. For 3x3 and larger, the calculator uses cofactor expansion along the first row. The determinant tells you whether the matrix is invertible (det != 0) and represents the scaling factor of the linear transformation the matrix defines.

A matrix has an inverse only if it is square (same number of rows and columns) and its determinant is not zero. The inverse of A, denoted A^(-1), satisfies A x A^(-1) = I (the identity matrix). The calculator checks invertibility and computes the inverse using the adjugate method or row reduction.

The calculator supports matrices from 2x2 up to 10x10. You can specify custom row and column counts for rectangular matrices. For operations requiring square matrices (determinant, inverse), only square matrices are accepted. The grid interface makes entering values straightforward for any size.