(adsbygoogle = window.adsbygoogle || []).push({}); Rank(A)= Trace(AA*) ??

I have two questions and I hope it is acceptable...Seemingly unrelated, though I came to wonder about the first while thinking the second. Thanks

1)Is this statement true? or is there a statement that relates Rank(A) and Trace(??)

2) AB-BA=I (When does this identity hold if at all? Field can be closed or Z/Z2, or etc)

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# Rank(A)= Trace(AA*) ?

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