(a) If two matrices are matrix equivalent and invertible, must their inverses be matrix equivalent? (b) If...

Question:

(a) If two matrices are matrix equivalent and invertible, must their inverses be matrix equivalent?
(b) If two matrices have matrix equivalent inverses, must the two be matrix equivalent?
(c) If two matrices are square and matrix equivalent, must their squares be matrix equivalent?
(d) If two matrices are square and have matrix equivalent squares, must they be matrix equivalent?