# What are the Properties of determinants?

## Properties of Determinants

1. The value of the determinant of a matrix doesn’t change if we transpose this matrix (change rows to columns)
2. If we multiply a scalar a to an nxn matrix A, then the value of the determinant will change by a factor a∧n
3. This makes sense since we are free to choose by which row or column we will expand the determinant. If we choose the one containing only zeroes, the result, of course, will be zero. And – it must be zero for all other possible expansions, too.
4. If two determinants differ by just one column, we can add them together by just adding up these two columns.