Trace of Sum of Matrices is Sum of Traces

Theorem
Let $\mathbf A = \sqbrk a_n$ and $\mathbf B = \sqbrk b_n$ be square matrices of order $n$.

let $\mathbf A + \mathbf B$ denote the matrix entrywise sum of $\mathbf A$ and $\mathbf B$.

Then:
 * $\map \tr {\mathbf A + \mathbf B} = \map \tr {\mathbf A} + \map \tr {\mathbf B}$

where $\map \tr {\mathbf A}$ denotes the trace of $\mathbf A$.