Exercise 63.4.2. Given maps

$\Lambda ^{\oplus m} \xrightarrow {a} \Lambda ^{\oplus n} \quad \text{and}\quad \Lambda ^{\oplus n} \xrightarrow {b} \Lambda ^{\oplus m}$

show that $\text{Tr}(ab) = \text{Tr}(ba)$.

Comment #6784 by 杜长江 on

Maybe the source of $a$ should be $\Lambda^m$? Otherwise $ab$ is not well defined. (Moreover, to make sure the latter definition of trace is well defined, one needs $a$ to be a map from $\Lambda^m$ to $\Lambda^n$)

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