Problem 4. If A = [aij] is an nxn matrix, then the trace of A, Tr(A), is defined as the sum of all the elements on the main diagonal of A, i.e., Tr(A) = > a;;. Show each of the following: i=1 (iii) Tr(AB) = Tr(BA) (iv) Tr(A") = Tr(A) (v) Tr(AT A) > 0

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