Is this true or false, and what is the explanation?

57 Views Asked by At

If A is a square matrix, does det(-A) = -det(A)?

2

There are 2 best solutions below

2
On

Changing the sign of a row or column changes the sign of the determinant.

Changing the sign of $n$ rows or columns multiplies the determinant by $(-1)^n$.

Therefore ...

0
On

As $$|kA|=k^n|A|$$ so If $A$ is a square matrix of odd order then $$|-A|=-|A|$$ but in case of even order $$|-A|=|A|$$