Question

Let M and N be two 3 x 3 matrices such that MN = NM. Further, if M ≠ N² and M² = N², then 

(A) determinant of (M² + MN²) is 0

(B) there is a 3 x 3 non-zero matrix U such that (M² + MN²)U is the zero matrix

(C) determinant of (M² + MN²) ≥ 1

(D) for a 3 x 3 matrix U, if (M² + MN²)U equals the zero matrix then U is the zero matrix

Answer 1

(A) determinant of (M² + MN²) is 0

(B) there is a 3 x 3 non-zero matrix U such that (M² + MN²)U is the zero matrix