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If A; B are non singular square matrices...

If A; B are non singular square matrices of same order; then `adj(AB) = (adjB)(adjA)`

A

Statement -1 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 Statement -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:
A
We have,
`(AB)(adj AB)=abs(AB)I …(i) [:' A (adj A)=absAI]`
`(AB) (adj B adj A)=A(B adj B) adjA`
`rArr (AB)(adjB adjA)=(A (absBI))adjA [:' B(adj B )=absBI]`
`rArr (AB)(adj B adj A)=absB(A adj A)`
`rArr (AB) (adj B adjA)=absBabsAI=abs(AB)I ...(ii)`
From (i) and (ii), we get
`:. adj(AB) =(adjB)(adjA)`
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