Determinant Calculator
The determinant tells whether a square matrix can be inverted: it is zero exactly when the rows are linearly dependent. Type the matrix with one row per line.
How to use it
- Type matrix A, and matrix B if the operation needs two matrices.
- Choose the operation: sum, product, determinant, inverse and more.
- Read the exact result, or tick show decimals.
Frequently asked questions
When can two matrices be multiplied?
When the number of columns of A equals the number of rows of B. The product of an m×n matrix by an n×p matrix is m×p, and in general A×B is different from B×A.
Why use exact fractions?
Decimals pile up rounding errors: a determinant that should be 0 can come out as 1e-16, and a singular matrix then looks invertible. With fractions every step is exact.
What are rank and reduced row echelon form?
Gauss-Jordan elimination turns the matrix into reduced row echelon form, with a leading 1 in each pivot row. The rank is the number of pivots: the number of linearly independent rows.
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