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If `A ,\ B` are square matrices of order `3,\ A` is non-singular and `A B=O` , then `B` is a (a) null matrix (b) singular matrix (c) unit matrix (d) non-singular matrix

A

null matrix

B

singular matrix

C

unit matrix

D

non-singular matrix.

Text Solution

Verified by Experts

The correct Answer is:
A
It is given that `absAne0`.
So, `A^(-1)`exists.
Now,
`AB=O`
`rArr A^(-1) (AB) =A^(-1) O`
`rArr (A^(-1)A) B=OrArr IB =OrArr B=O`
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