Matrix Calculator

Perform matrix operations including addition, multiplication, transpose, determinant, inverse, and RREF with detailed step-by-step solutions.

Choose operation and configure matrices

Operation

Matrix A Rows

Matrix A Cols

Matrix B Rows

Matrix B Cols

Quick Examples:

Matrix A (2×2)

Matrix B (2×2)

Performed element-wise. Matrices must have identical dimensions. Addition is commutative and associative.

(A + B)[i,j] = A[i,j] + B[i,j]

Columns of first matrix must equal rows of second matrix. Generally not commutative but is associative.

(A × B)[i,j] = Σ A[i,k] × B[k,j]

Flips matrix along main diagonal. Rows become columns and vice versa. Transpose of transpose returns original matrix.

(A^T)[i,j] = A[j,i]

A scalar value that encodes certain properties of a square matrix. Zero determinant means matrix is singular (not invertible).

2×2: det(A) = ad - bc

Larger matrices: Use cofactor expansion or elimination