please do 8-11 explain it with some details thx step by step would be better.

(V, W), II all a12 and B = b11 b12 an inner 8. Let A = a21 a22 b21 622 be vectors in M2(R). Show that the mapping (A, B) = allbil does not define a valid inner product on M2(R). Which of the four properties of an inner product, if any, do ce V, hold? Justify your answer. 9. Referring to A and B in Problem 8, show that the mapping 0 if (A, B) = det(AB) does not define a valid inner product on M2 (R). Which nner of the four properties of an inner product, if any, do hold? Justify your answer. ner 10. Referring to A and B in Problem 8, show that the the mapping 2 (A, B) = allb22 + a12b21 + a21b12 + a22611 via does not define a valid inner product on M2 (R). Which of the four properties of an inner product, if any, do hold? Justify your answer. 11. Referring to A and B in Problem 8, show that the e mapping (A, B) = allbil + a12b12 + a21621 + a22622 (5.1.13) defines a valid inner product in M2 (R)