Suppose A and B are $5\times 5$ matrices with $\det(A) = -1/3$ and $\det(B) = 6$, find the determinant of $ 2AB$.
Solution:
$$= \det(2AB) $$ $$= 2^5 \det(A)\det(B) $$ $$= (32)(-1/3)(6)$$ $$= -64$$
I understand how all of this works, except for where $2^5$ comes from, can anyone explain how this happens?