Question
Suppose $V$ is finite-dimensional and $S, T \in \mathcal{L}(V) .$ Prove that $S T=I$ if and only if $T S=I$.
Step 1
We need to prove that for two linear transformations $S$ and $T$ on a finite-dimensional vector space $V$, the condition $ST = I$ (where $I$ is the identity map on $V$) implies $TS = I$, and vice versa. Show more…
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