Square matrices are similar if they represent the same transformation, but each with respect to the same ending as starting basis. That is, RepB1,B1 (t) is similar to RepB2,B2 (t).
(a) Give a definition of matrix similarity like that of Definition 2.3.
(b) Prove that similar matrices are matrix equivalent.
(c) Show that similarity is an equivalence relation.
(d) Show that if T is similar to  then T2 is similar to 2, the cubes are similar, etc. Contrast with the prior exercise.
(e) Prove that there are matrix equivalent matrices that are not similar.