True or False? If False, you should come up with a counterexample.

Suppose \(A\) and \(B\) are \(n\times n\) matrices (\(n\geq 2\)).

(a)
\(\det {(AB)}=\det {A}\det {B}\)
True False
(b)
If \(\det {A}=\frac {1}{\det {B}}\), then \(A=B^{-1}\).
True False
(c)
\(\det {(A+B)}=\det {A}+\det {B}\).
True False
(d)
If \(A=2B\), then \(\det {A}=2\det {B}\).
True False
(e)
If \(A=-B\), then \(\det {A}=-\det {B}\) when \(n\) is odd, and \(\det {A}=\det {B}\) when \(n\) is even.
True False