8. Let A, B, C be n x n matrices with real entries. Determine if the following statements

are true or false. Provide a brief explanation in each case.

(a) If R = RREF(A), then det(R) = det(A).

(b) If det(A)=det (B), then A= B.

(c) det(A + B) = det(A)+det(B).

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(d) If det (AB) = 0, then det(A) = 0 or det (B) = 0.

(e) If A, C and ABC are invertible, then B is invertible.