For an n × n matrix A, the main counter diagonal elements are a1n, a2n-1, . . . ,an1. The sum of the main counter diagonal elements is denoted Mcd(A), and we have

meaning the sum of all the entries of A whose subscripts add to n + 1.
(a) Prove: Mcd(cA) = c Mcd(A), where c is a real number.
(b) Prove: Mcd(A + B) = Mcd(A) + Mcd(fi).
(c) Prove: Mcd(A7) = Mcd(A).
(d) Show by example that Mcd(AB) need not be equal to Mcd(SA).

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