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

Question

If A and B are two 3 × 3 matrices such that their product A B is a null matrix then (A) det. A ≠ 0 ⇒ B must be a null matrix. (B) det. B ≠ 0 ⇒ 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.

Tardigrade Admin · Accepted Answer

Correct answer is (a) det. A ≠ 0 ⇒ B must be a null matrix.Correct answer is (b) det. B ≠ 0 ⇒ 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.

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

det. $A \neq = 0 \Rightarrow B$ must be a null matrix.

det. $B \neq = 0 \Rightarrow A$ must be a null matrix.

If none of $A$ and $B$ are null matrices then atleast one of the two matrices must be singular.

If neither det. A nor det. B is zero then the given statement is not possible.

Q. If A and B are two 3×3 matrices such that their product AB is a null matrix then

det. A=0⇒B must be a null matrix.

det. B=0⇒A must be a null matrix.

If none of A and B are null matrices then atleast one of the two matrices must be singular.

If neither det. A nor det. B is zero then the given statement is not possible.

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

det. $A \neq = 0 \Rightarrow B$ must be a null matrix.

det. $B \neq = 0 \Rightarrow A$ must be a null matrix.

If none of $A$ and $B$ are null matrices then atleast one of the two matrices must be singular.