(12 marks in total) For anyr linear transformation (,0 : MAR) ) MAR), we define a new linear transformation (.02 : MAR] > MAR] such that for ever).r block matrix A B X:(0 D)' where A, B, (LB E M2[R). we set X 2 90M) 90(3) _ 5"\" ' (90(0) 50(9)) [You are not required to prove (pg is linear.) (a) (4 marks) Prove that for any two linear transformations (,0 : MAR) > Mz-[R] and 1f; : MZUR) ) MAR), we have ($09012 =1b2 0902- (b)(4 marks) Prove that if (p : MAR) ) MQUR) is injective, then so is (pg. (c) {4 marks) Use the result of {b} to show that if (p is surjective, then 502 is sLujective