Matrix Calculator
Perform operations on matrices up to 6×6 with step-by-step solutions.
Free & unlimited
Matrix A
2×2Rows
Cols
Matrix B
2×2Rows
Cols
All processing happens in your browser. No data is sent to any server.
About this tool
- 1
Set matrix dimensions
Choose the number of rows and columns for your matrix (or matrices for binary operations).
- 2
Enter values
Fill in the matrix cells with numeric values. Tab between cells for quick entry.
- 3
Choose an operation
Select addition, multiplication, transpose, determinant, inverse, or other operations.
- 4
View the result
See the resulting matrix displayed in standard mathematical notation with step-by-step calculations.
- Matrix multiplication requires the number of columns in the first matrix to equal the number of rows in the second.
- Only square matrices (same rows and columns) have determinants and inverses.
- A matrix with a determinant of 0 is singular and has no inverse.
- The transpose of a matrix swaps its rows and columns - useful for solving systems of equations.
- Addition, subtraction, and scalar multiplication
- Matrix multiplication with dimension validation
- Transpose, determinant, and inverse calculations
- Step-by-step solution display
- Adjustable matrix dimensions up to 10x10
- Solve linear algebra homework and verify matrix calculations.
- Compute transformations for computer graphics programming.
- Calculate determinants for systems of linear equations.
- Verify inverse matrices for cryptography and data science applications.
Matrix multiplication A x B requires that A's column count equals B's row count. For example, a 2x3 matrix can multiply a 3x4 matrix (result is 2x4), but not a 2x2 matrix.
A zero determinant means the matrix is singular - it has no inverse, its rows/columns are linearly dependent, and the corresponding system of equations has either no solution or infinitely many solutions.
The identity matrix has 1s on the diagonal and 0s elsewhere. Multiplying any matrix by the identity matrix returns the original matrix - it is the matrix equivalent of multiplying by 1.