# Problem of the Week #363 - April 6, 2021

#### Euge

##### MHB Global Moderator
Staff member
Here is this week's POTW:

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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 $T$?
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