# How do I calculate the determinant of a 4x4 Matrix?

Dec 28, 2017

See explanation...

#### Explanation:

Note that the determinant of a matrix is unaltered by adding or subtracting any multiple of one row and any other row.

The absolute value of the determinant is retained, but with opposite sign if any two rows or columns are swapped.

The easiest practical manual method to find the determinant of a $4 \times 4$ matrix is probably to apply a sequence of the above changes in order to get the matrix into upper triangular form. Then the determinant is just the product of the diagonal elements.