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Problem of the Week #363 - April 6, 2021

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MHB Global Moderator
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Jun 20, 2014
Here is this week's POTW:

Let $\Bbb F$ be a field. Prove that there is a unique linear functional $T : M_n(\Bbb F) \to \Bbb F$ such that

1. $T(I_n) = n$
2. $T(XY) = T(YX)$ for all $X, Y\in M_n(\Bbb F)$

What is the name for $T$?

Remember to read the POTW submission guidelines to find out how to submit your answers!