Matrix Calculator
Perform matrix operations: add, subtract, multiply, find determinant, transpose, and inverse. See also Percentage Calculator and Exponent Calculator.
How to Use the Matrix Calculator
Select the matrix size (2×2 or 3×3) and the operation you want to perform. Enter values into the matrix grids and click Calculate. For addition, subtraction, and multiplication, you need two matrices. For determinant, transpose, and inverse, only Matrix A is used. The calculator shows the result as a matrix or scalar value.
Matrix Formulas
Addition: C[i][j] = A[i][j] + B[i][j]
Subtraction: C[i][j] = A[i][j] - B[i][j]
Multiplication: C[i][j] = Σ A[i][k] × B[k][j]
Determinant (2×2): ad - bc
Transpose: Aᵀ[i][j] = A[j][i]
Inverse: A⁻¹ = adj(A) / det(A)
Example
Matrix A = [[1, 2], [3, 4]]
Matrix B = [[5, 6], [7, 8]]
A + B = [[6, 8], [10, 12]]
A × B = [[19, 22], [43, 50]]
det(A) = 1×4 − 2×3 = −2
Frequently Asked Questions
What is a matrix determinant?
The determinant is a scalar value computed from a square matrix. It indicates whether the matrix is invertible (non-zero determinant) and is used in solving systems of linear equations, finding area/volume, and eigenvalue problems.
When does a matrix not have an inverse?
A matrix has no inverse when its determinant is zero. Such a matrix is called singular or degenerate. This means the rows (or columns) are linearly dependent.
Is matrix multiplication commutative?
No. In general, A × B ≠ B × A. The order of multiplication matters. However, matrix addition is commutative: A + B = B + A.