Let A and B be two 3 3 non-zero real matrices such that AB is a z… - Vidyadip

MCQ

Let $A$ and $B$ be two $3 \times 3$ non-zero real matrices such that $AB$ is a zero matrix. Then.

A
The system of linear equations $AX =0$ has a unique solution
✓
The system of linear equations $AX =0$ has infinitely many solutions
C
$B$ is an invertible matrix
D
$\operatorname{adj}$ $(A)$ is an invertible matrix

✓

Answer

Correct option: B.

The system of linear equations $AX =0$ has infinitely many solutions

b
$AB =0 \Rightarrow| AB |=0$

If $| A | \neq 0, B =0$ (not possible)

If $| B | \neq 0, A =0$ (not possible)

Hence $| A |=| B |=0$

$AX =0$ has infinitely many solutions

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