Determining the determinant of a matrix

Question

So i was given this question

Find det A if A is $3 × 3$ and $det(2A) = 6$. Under what conditions is det(−A) = det A?

I'm used to dealing with questions that give a matrix to solve, but this question seems to confuse me.

I started off by trying to use the theorem if A is a $n × n$ matrix, then $det(uA)$ $=$ $u^ndet A$ for any number u.

But i get confused as to what exactly is u and how to apply the theorem

Answer 1

Using your theorem we can write $\det(2A) = 2^3\det(A) = 6$ so that $\det(A) = \frac{6}{2^3} = \frac{6}{8} = \frac{3}{4}$.

Answer 2

The value of $\det(A)$ is easy to know by your formula.It's $3/4$. For the second part of the question, use the same formula and choose $u=-1$. Clearly then you will have $\det (-A)=(-1)^n \det A$. Now what values of $n$ would make the right side of the above equation $-\det A$?