Online Matrix Calculator
Perform matrix arithmetic with full linear algebra support: matrix multiplication, determinant calculation, Gaussian elimination, inverse matrix, and transposition.
Matrix A
Matrix B
Operation Result: A + B (Addition)
How to use
- Set matrix dimensions (rows and columns).
- Fill numeric values into matrix cells.
- Choose desired matrix operation (det, inverse, multiply, add, transpose).
- View resulting output matrix alongside clear algebraic steps.
Standard Matrix Operations
Determinant det(A): evaluated for square matrices (for 2×2: ad - bc).
Matrix Multiplication: product of A (m×k) and B (k×n) yields resulting matrix m×n.
Transposition Aᵀ: interchanges rows and columns.
Inverse Matrix A⁻¹: defined exclusively for non-singular square matrices with det(A) ≠ 0.
Calculation Methodology
Calculations apply Gaussian elimination, cofactor expansion along rows/columns, and Gauss-Jordan matrix inversion algorithms.
Frequently Asked Questions
What does a zero determinant signify?
A zero determinant indicates a singular matrix whose rows or columns are linearly dependent.
When is matrix multiplication permitted?
Only when the number of columns in the first matrix equals the number of rows in the second matrix.
Is matrix multiplication commutative?
No, matrix multiplication is non-commutative in general: A*B rarely equals B*A.
Which matrices have an inverse?
Only square matrices with a non-zero determinant (det ≠ 0).
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