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Q.

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

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a

B is an invertible matrix

b

the system of linear equations AX = O has infinitely many solutions

c

adj (.A) is an invertible matrix

d

the system of linear equations AX = 0 has a unique solution

answer is B.

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Detailed Solution

AB=O⇒|AB|=0⇒|A||B|=0
⇒ Either |A|=0 or |B|=0
If |A|≠0,B=O (not possible); If |B|≠0,A=0(not possible)
Hence, |A|=|B|=0
⇒AX=0 has infnitely many solutions.
 

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