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Statement-1 For a singular matrix A , if...

Statement-1 For a singular matrix `A , if AB = AC rArr B = C`
Statement-2 If `abs(A) = 0,` then` A^(-1)` does not exist.

A

Statement- is true, Statement -2 is true, Statement-2
is a correct explanation for Statement-1

B

Statement-1 is true, Statement-2 is true, Statement - 2
is not a correct explanation for Stamtement-1

C

Statement 1 is true, Statement - 2 is false

D

Statement-1 is false, Statement-2 is true

Text Solution

Verified by Experts

The correct Answer is:
D
`A^(-1) ` exists only for non-singular matrix
`AB= AC rArr A^(-1) (AB) = A^(-1) (AC) `
`rArr (A^(-1) A ) B= (A^(-1)A) C`
`rArr IB = IC`
`rArr B= C, ` if `A^(-1)` exist
`therefore abs(A) ne 0`
Statement- 2 is false and Statement-2 is true.
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