Question

If $A$ and $B$ are two $3 \times 3$ matrices such that their product $A B$ is a null matrix then

• A. det. $A \neq 0 \Rightarrow B$ must be a null matrix.
• B. det. $B \neq 0 \Rightarrow A$ must be a null matrix.
• C. If none of $A$ and $B$ are null matrices then atleast one of the two matrices must be singular.
• D. If neither det. A nor det. B is zero then the given statement is not possible.

Answer 1

Answer: (A), (B), (C), (D)

Correct answer is (a) det. $A \neq 0 \Rightarrow B$ must be a null matrix.Correct answer is (b) det. $B \neq 0 \Rightarrow A$ must be a null matrix.Correct answer is (c) If none of $A$ and $B$ are null matrices then atleast one of the two matrices must be singular.Correct answer is (d) If neither det. A nor det. B is zero then the given statement is not possible.