The trace of an nxn matrix A = (aij) is the sum of the diagonal elements, Show that A and B are n x n matrices, then tr(AB) = tr(BA). Show that tr(A+B) = tr(A) + tr(A). Show that for any scalar a € R,...

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Extracted text: The trace of an nxn matrix A = (aij) is the sum of the diagonal elements, Show that A and B are n x n matrices, then tr(AB) = tr(BA). Show that tr(A+B) = tr(A) + tr(A). Show that for any scalar a € R, then tr(aA) = atr(A). Prove that there are no n xn matrices A and B such that AB – BA =I I is the n x n identity matrix.