Let M and N be two 3 × 3 matrices such that MN = NM . Further, if M ≠ N 2 and M 2 = N 4 …
Mathematics · JEE Advanced · NTA Exams — Matrices and Determinants
Let M and N be two 3 × 3 matrices such that MN = NM. Further, if M ≠ N2 and M2 = N4, then
- determinant of (M2 + MN2) is 0
- there is a 3 × 3 non-zero matrix U such that
(M2 + MN2)U is the zero matrix - determinant of (M2 + MN2) ≥ 1
- for a 3 × 3 matrix U, if (M2 + MN2)U equals the zero matrix then U is the zero matrix.
Answer
(B) there is a 3 × 3 non-zero matrix U such that ( M 2 + MN 2 ) U is the zero matrix
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