Q27

MCQ2 marks, −0.67

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

(A)

$\text{rank}(AB) = \text{rank }(A) \text{rank }(B)$

(B)

$\text{det}(AB) = \text{det}(A) \text{det}(B)$

(C)

$\text{rank}(A + B) \leq \text{rank }(A) + \text{rank }(B)$

(D)

$\text{det}(A + B) \leq \text{det}(A) + \text{det} (B)$

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