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.
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.
Hint: take the trace of $AB-BA$ and compare with the trace of the identity matrix.
I know this one from my Linear Algebra course. hint: Take a look at the trace of the matrix $X = AB - BA$.