Suppose that A is an nxn invertible matrix. Prove the following statements:  (a) If there exists an nxn matrix D such that AD=I_n then D=A^-1. (b) If B and C are matrices such that A(B-C)=0 (where 0 is a zero matrix of appropriate size), then B=C.  Hint: Both of these are simplier to prove using matrix algebra rather than the definition of matrix multiplication.  I_n is the identity matrix and A^-1 is A inverse matrix.

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