True or False? If False, you should come up with a counterexample.
Suppose \(A\) and \(B\) are \(n\times n\) matrices (\(n\geq 2\)).
- 1.
- \(\det {(AB)}=\det {A}\det {B}\)
True False
- 2.
- If \(\det {A}=\frac {1}{\det {B}}\), then \(A=B^{-1}\).
True False
- 3.
- \(\det {(A+B)}=\det {A}+\det {B}\).
True False
- 4.
- If \(A=2B\), then \(\det {A}=2\det {B}\).
True False
- 5.
- If \(A=-B\), then \(\det {A}=-\det {B}\) when \(n\) is odd, and \(\det {A}=\det {B}\) when \(n\) is even.
True False