What's the trace of a Matrix?

Trace of a square matrix.

The trace of a square matrix is defined as the sum of the diagonal elements.

Let a square matrix, $A=\left[\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right]$

So, the trace of the matrix, $\mathrm{tr}\left(A\right)=a+e+i$

Hence, the trace of the matrix is the sum of all the diagonal elements.