Matrix Calculator
Perform comprehensive matrix operations including addition, subtraction, multiplication, determinant calculation, inverse, transpose, and more with step-by-step solutions.
Matrix Calculator
Free online matrix calculator. Calculate various matrix operations including transpose, inverse, determinant, addition, subtraction, multiplication, and scalar operations with step-by-step solutions.
Matrix A
Matrix B
Single Matrix Operations
Multiple Matrix Operations
Transpose of a Matrix
The transpose of a matrix is obtained by rotating the matrix elements around the diagonal. If an element is at position (i,j), its position in the transposed matrix will be (j,i).
For example, the transpose of:
| 1 | 2 | 3 |
| 4 | 5 | 6 |
| 7 | 8 | 9 |
becomes:
| 1 | 4 | 7 |
| 2 | 5 | 8 |
| 3 | 6 | 9 |
Determinant of a Matrix
The determinant is a dimensionless value calculated from the elements of a square matrix. It's used to solve systems of linear equations and find matrix inverses.
For a 2×2 matrix:
| a | b |
| c | d |
Matrix Operations
Addition/Subtraction: Matrices must have the same dimensions
Multiplication: Number of columns in first matrix must equal number of rows in second matrix
Inverse: Only exists for square matrices with non-zero determinant
Transpose: Can be applied to any matrix