Matrix Determinant Calculator
Choose the size and enter the matrix values — for 2x2 you get the ad − bc formula and for 3x3 the cofactor expansion steps with the determinant.
Matrix (for 2x2, leave the third row/column empty and select size 2)
How to use
- Select the matrix size (2x2 or 3x3) and enter values in all cells.
- For 2x2 the ad − bc formula is shown with your numbers filled in.
- For 3x3 the cofactor expansion by the first row is shown step by step.
- Read the determinant at the end of the steps.
Note: If the determinant is 0, the matrix is singular — it has no inverse and the system is either inconsistent or has infinite solutions.
Tips
- A zero determinant means the matrix has no inverse and cannot give a unique solution.
- For 2x2, ad − bc is all you need — that one is worth memorizing.
- Double-check signs in cofactor expansion; sign errors are the most common mistake.