Proof about similar matrices

[mooshupork34]

These two proofs was troubling me and I have a quiz on them tomorrow, so if anyone could explain them to me, I would really appreciate it! Thanks in advance.

A matrix B is similar to a matrix A if there exists some (nonsingular) matrix P such that PAP^-1 = B.

Show that:
a) If B is similar to A, then A is similar to B.
b) Show that if A and B are similar, then the determinant of A = the determinant of B.

 

[Unco]

a) \(\displaystyle PAP^{-1} = B \Rightarrow A = P^{-1}BP = QBQ^{-1}\) with \(\displaystyle Q = P^{-1}\).

b) Determinants commute; \(\displaystyle \det(A^{-1}) = \frac{1}{\det(A)}\).