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Question:

Let M and N be two 3x3 matrices such that MN = NM. Further, if M ≠ N² and M² = N⁴, then

Determinant of (M² + MN²) is 0

Determinant of (M² + MN²) ≥ 1

There is a 3x3 non-zero matrix U such that (M² + MN²)U is the zero matrix

For a 3x3 matrix U, if (M² + MN²)U equals the zero matrix, then U is the zero matrix

Solution:

M² = N⁴ ⇒ M² - N⁴ = 0 ⇒ (M - N²)(M + N²) = 0