5. Let B be an invertible n X 12 matrix. Dene (1)3 : RM\" > RM\" by (PB-(A) = BlAB. (a) Prove that (1)3 is an isomorphism by showing that (D3 is linear and bijective. What is its inverse transformation? (b) Now, dene TB : Rm\" > Rnxn by TB(A) = (1)3(A) A. Give a nice property that determines if A E ker(T3). (C) Suppose now that n = 3 and that every diagonal n X n matrix D is in ker(TB). What can you say about the matrix B