question 6

6. Let A M. (R). Prove or provide a counter example: (n) If A - A =0 then dot A = 0 ordet A = 1 (b) If A-2A = 0 then det A = 0 ordet A = 2 (c) The RREF of A is equal to the RREF of AT 1 (d) If there exists an invertible matrix Pe M, such that APBP, then det (A) - det (B). Note: If such P existe, A and B are said to be similar (o) Il det (A) - det (B) then A and Bartow equivalent (1) IF A-1, then must be even