Question: The trace of an n X n matrix A = [aij] is the sum of the entries on its main diagonal and is denoted by

The trace of an n X n matrix A = [aij] is the sum of the entries on its main diagonal and is denoted by tr(A). That is,
tr(A) = a11 + a22 + · · · + ann
If A and B are n × n matrices, prove the following properties of the trace:
(a) tr (A + B) = tr (A) + tr (B)
(b) tr (kA) = ktr (A), where k is a scalar

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