Question: The trace of a square matrix A, denoted tr A, is the sum of the elements on the main diagonal of A. Show that, if

The trace of a square matrix A, denoted tr A, is the sum of the elements on the main diagonal of A. Show that, if A and B are n × n matrices:
(a) tr(kA) = k tr(A) for any number k.
(b) tr(AAT) is the sum of the squares of all entries of A.

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