Pick a matrix size, enter the values, and get the determinant instantly — with the expansion shown for 3×3.
Matrix Determinant Calculator
How It’s Calculated
For a 2×2 matrix [[a,b],[c,d]], the determinant is simply ad − bc. For a 3×3 matrix, this calculator expands along the first row using cofactors — each entry in the top row is multiplied by the determinant of the 2×2 matrix left over when you delete that entry’s row and column, with alternating signs (+, −, +).
Worked Example
For [[2,0,1],[3,1,2],[1,0,3]]: det = 2(1×3 − 2×0) − 0(3×3 − 2×1) + 1(3×0 − 1×1) = 2(3) − 0 + 1(−1) = 6 − 1 = 5.
Frequently Asked Questions
Q: What does it mean if the determinant is 0?
The matrix is singular — it has no inverse, and the system of equations it represents either has no solution or infinitely many.
Q: Does the order I expand along matter?
No — expanding along any row or column gives the same determinant. This tool always expands along the first row for consistency.
Determinants decide whether a matrix can be inverted — covered right after Matrices in the 2nd PUC syllabus. Read the Matrices chapter guide →