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Let M and N be two $$3 \times 3$$ matrices such that MN = NM. Further, if $$M \neq N^2$$ and $$M^2 = N^4$$, then
determinant of $$(M^2 + MN^2)$$ is 0
there is a $$3 \times 3$$ non-zero matrix UU such that $$(M^2 + MN^2)$$ U is the zero matrix
determinant of $$(M^2 + MN^2) \geq 1$$
for a $$3 \times 3$$ matrix UU, if $$(M^2 + MN^2)$$U equals the zero matrix then U is the zero matrix
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