Matrix Calculator
Perform matrix operations including addition, multiplication, determinant, inverse, and transpose.
A matrix calculator performs common matrix operations including determinant, inverse, transpose, addition, and multiplication.
Examples
2x2 Determinant
Matrix Addition
Transpose
Frequently Asked Questions
When can I find a matrix inverse?
What are the rules for matrix multiplication?
What is the determinant used for?
Quick Tips
- •Double-check your inputs — small errors lead to incorrect results.
- •Use semicolons to separate rows and commas to separate values within a row.
- •For multiplication, ensure the number of columns in Matrix A equals the number of rows in Matrix B.
A matrix calculator performs common matrix operations including determinant, inverse, transpose, addition, and multiplication.
How to Use This Calculator
Enter matrix values with commas separating columns and semicolons separating rows (e.g. 1,2;3,4 for a 2x2 matrix). Select an operation. For multiply and add, enter a second matrix.
Understanding the Formula
Determinant: expansion by cofactors. Inverse: A⁻¹ = adj(A)/det(A). Transpose: swap rows and columns. Multiply: C[i][j] = Σ A[i][k]×B[k][j].
Examples
2x2 Determinant
|1,2;3,4| = 1×4 - 2×3 = -2
Matrix Addition
[1,2;3,4] + [5,6;7,8] = [6,8;10,12]
Transpose
Transpose of [1,2,3;4,5,6] = [1,4;2,5;3,6]
Frequently Asked Questions
When can I find a matrix inverse?
Only square matrices with a non-zero determinant have an inverse. If the determinant is zero, the matrix is singular.
What are the rules for matrix multiplication?
The number of columns of the first matrix must equal the number of rows of the second. An m×n matrix times an n×p matrix produces an m×p matrix.
What is the determinant used for?
The determinant indicates if a matrix is invertible (non-zero det), measures volume scaling in linear transformations, and appears in solving systems of equations.
Assumptions & Limitations
- Assumes well-formed matrix input with consistent row lengths.
- Inverse requires a square matrix with a non-zero determinant.
- Results may show floating-point approximations for irrational numbers.