Question

Let M and N be two 3 × 3 matrices such MN = NM. Further, if M ≠ N2 and M2 = N4, then (A) Determinant of (M2 + MN2) is 0. (B) There is a 3 × 3 non-zero matrix U such that (M2 + MN2)U is the zero matrix. (C) Determinant of (M2 + MN2) ≠ 1. (D) For a 3 × 3 matrix U, if (M2 + MN2)U equals the zero matrix then U is the zero matrix.

Answer 1

Answer:

Let M and N be two 3 × 3 matrices such MN = NM. Further, if M ≠ N2 and M2 = N4, then (A) Determinant of (M2 + MN2) is 0. (B) There is a 3 × 3 non-zero matrix U such that (M2 + MN2)U is the zero matrix. (C) Determinant of (M2 + MN2) ≠ 1. (D) For a 3 × 3 matrix U, if (M2 + MN2)U equals the zero matrix then U is the zero matrix.