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If A and B are non-singular square matri...

If `A` and `B` are non-singular square matrices of same order then `adj(AB)` is equal to

A

(adj A) (adj B)

B

(adj A) + (adj B)

C

(adj A) - (adj B)

D

(adj B) (adj A)

Text Solution

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The correct Answer is:
D
Since, A and B be two invertible square matrices each of order n, then `(AB)^(-1) = (B^(-1))(A^(-1))`
`rArr (adj(AB))/(|AB|)=(adj B)/(|B|).(adj A)/(|A|)`
Since `|AB| = |B||A|`
adj (AB) = (adj B)(adj A)
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