Let $A$ and $B$ be two $n \times n$ matrices over real numbers. Let $\text{rank}(M)$ and $\det(M)$ denote the rank and determinant of a matrix $M$, respectively. Consider the following statements. I. $\text{rank}(AB) = \text{rank}(A) \text{rank}(B)$ II. $\det(AB) = \det(A) \det(B)$ III. $\text{rank}(A + B) \le \text{rank}(A) + \text{rank}(B)$ IV. $\det(A + B) \le \det(A) + \det(B)$ Which of the above statements are TRUE?

Let A and B be two n n matrices over real numbers. Let rank(M) and (M) denote the rank and determinant of a matrix M, respectively. Consider the following statements. I. rank(AB) = rank(A) rank(B) II. (AB) = (A) (B) III. rank(A + B) rank(A) + rank(B) IV. (A + B) (A) + (B) Which of the above statements are TRUE?

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