Indicate whether each statement is always true or sometimes false. Justify your answer by giving a logical

Question:

Indicate whether each statement is always true or sometimes false. Justify your answer by giving a logical argument or a counterexample.
(a) A matrix cannot be similar to itself.
(b) If A is similar to B, and B is similar to C, then A is similar to C.
(c) If A and B are similar and B is singular, then A is singular.
(d) If A and B are invertible and similar, then A-1 and B-1 are similar.