Putnam 2015/ A6

Mathematical Competitions
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Tolaso J Kos
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Putnam 2015/ A6

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Post by Tolaso J Kos »

Let $n$ be a positive integer. Suppose that $A,B,$ and $M$ are $n\times n$ matrices with real entries such that $AM=MB,$ and such that $A$ and $B$ have the same characteristic polynomial. Prove that $\det(A-MX)=\det(B-XM)$ for every $n\times n$ matrix $X$ with real entries.
Imagination is much more important than knowledge.
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