Question: If A = [ajj] is an n Ã n matrix, then the trace of A, Tr(A), is defined as the sum of all elements on

If A = [ajj] is an n Ã— n matrix, then the trace of A, Tr(A), is defined as the sum of all elements on the main diagonal of A,

Show each of the following:
(a) Tr(cA) = c Tr(A), where c is a real number
(b) Tr(A + B) = Tr(A) + Tr(B)
(c) Tr(AB) = Tr(BA)
(d) Tr(AT) = Tr(A)
(e) Tr(ATA) ‰¥ 0

Tr(A)

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