Matrix Inverse Calculator
Enter the matrix — get the determinant, adjugate and inverse along with the A x A⁻¹ = I verification. If the determinant is 0, no inverse exists.
Matrix (for 2x2, leave the third row/column empty and select size 2)
How to use
- Select the matrix size and enter values in all cells.
- Check the determinant first — if it is 0, no inverse exists.
- For other matrices, see the adjugate and the inverse matrix.
- Verify the result with the A × A⁻¹ = I check shown below.
Note: The inverse only exists when the determinant is not 0. Method: A⁻¹ = adj(A) / det(A), where adj is the transpose of the cofactor matrix.
Tips
- Always check the determinant first — a zero determinant means no inverse exists.
- Multiply the matrix by its inverse for small cases to build intuition.
- Inverses are mainly used for solving linear equations — keep the method in your notes.