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Let $A$ and $B$ be square matrices of order $n$. Show that $AB - BA$ can never be equal to unit matrix.

How to approach above question. Please help.

José Carlos Santos
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Tortoise
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  • This does not hold in infinite dimensional settings and is crucial for quantum mechanics. It's a very interesting and surprising phenomenon. – Cameron Williams Aug 07 '17 at 14:20

2 Answers2

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Hint: take the trace of $AB-BA$ and compare with the trace of the identity matrix.

Reveillark
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I know this one from my Linear Algebra course. hint: Take a look at the trace of the matrix $X = AB - BA$.