Matrix
Matrix Addition Calculator
Add two matrices of the same size element by element — supports any size up to 12 × 12.
(A + B)ᵢⱼ = Aᵢⱼ + Bᵢⱼ
Also called add matrices · matrix sum
Math · 10 calculators
Matrix Calculators
Matrix addition, subtraction, multiplication, determinant, inverse, transpose and rank for any size.
Matrix
Matrix Subtraction Calculator
Subtract one matrix from another element by element (A − B) for matrices of equal size.
(A − B)ᵢⱼ = Aᵢⱼ − Bᵢⱼ
Also called subtract matrices · matrix difference
Matrix
Matrix Multiplication Calculator
Multiply two matrices (A × B) when the columns of A match the rows of B, with the result size shown.
(AB)ᵢⱼ = Σₖ Aᵢₖ·Bₖⱼ
Also called multiply matrices · matrix product
Matrix
Matrix Determinant Calculator
Compute the determinant of a square matrix of any size using LU decomposition with partial pivoting.
det(A) = product of pivots × (−1)^swaps
Also called determinant calculator · det of matrix
Matrix
Matrix Inverse Calculator
Find the inverse of a square matrix with Gauss–Jordan elimination, and check whether it is singular.
A·A⁻¹ = I
Also called inverse matrix · invert matrix
Matrix
Matrix Transpose Calculator
Transpose any matrix — swap its rows and columns — to get Aᵀ.
(Aᵀ)ᵢⱼ = Aⱼᵢ
Also called transpose matrix · a transpose
Matrix
Matrix Rank Calculator
Find the rank of a matrix — the number of linearly independent rows — by row reduction.
rank = number of non-zero rows in echelon…
Also called rank of matrix · row rank
Matrix
Identity Matrix Calculator
Generate an n × n identity matrix (ones on the diagonal, zeros elsewhere) and multiples of it.
Iᵢⱼ = 1 if i = j, else 0
Also called identity matrix · unit matrix
Matrix
2×2 Matrix Calculator
All-in-one 2×2 matrix calculator: determinant, inverse, transpose, trace and rank of a two-by-two matrix.
det = ad − bc
Also called 2x2 matrix · 2 by 2 matrix
Matrix
3×3 Matrix Calculator
All-in-one 3×3 matrix calculator: determinant, inverse, transpose, trace and rank of a three-by-three matrix.
det via cofactor expansion / row reduction
Also called 3x3 matrix · 3 by 3 matrix
Key matrix formulas
| Matrix Addition | (A + B)ᵢⱼ = Aᵢⱼ + Bᵢⱼ |
|---|---|
| Matrix Subtraction | (A − B)ᵢⱼ = Aᵢⱼ − Bᵢⱼ |
| Matrix Multiplication | (AB)ᵢⱼ = Σₖ Aᵢₖ·Bₖⱼ |
| Matrix Determinant | det(A) = product of pivots × (−1)^swaps |
| Matrix Inverse | A·A⁻¹ = I |
| Matrix Transpose | (Aᵀ)ᵢⱼ = Aⱼᵢ |
| Matrix Rank | rank = number of non-zero rows in echelon form |
| Identity Matrix | Iᵢⱼ = 1 if i = j, else 0 |
| 2×2 Matrix | det = ad − bc · A⁻¹ = (1/det)[d −b; −c a] |
| 3×3 Matrix | det via cofactor expansion / row reduction |
Matrix questions
How do I enter a matrix?
Type one row per line, separating values with spaces or commas. You can also separate rows with semicolons: 1 2; 3 4.
How do I enter a matrix?
Type one row per line, separating values with spaces or commas. You can also separate rows with semicolons: 1 2; 3 4.
How do I enter a matrix?
Type one row per line, separating values with spaces or commas. You can also separate rows with semicolons: 1 2; 3 4.
How do I enter a matrix?
Type one row per line, separating values with spaces or commas. You can also separate rows with semicolons: 1 2; 3 4.
How do I enter a matrix?
Type one row per line, separating values with spaces or commas. You can also separate rows with semicolons: 1 2; 3 4.