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If the adjoint of a 3 3 matrix P is 1 ...

If the adjoint of a 3 3 matrix P is 1 4 4 2 1 7 1 1 3 , then the possible value(s) of the determinant of P is (are) (A) 2 (B) 1 (C) 1 (D) 2

A

`-2`

B

`-1`

C

1

D

2

Text Solution

Verified by Experts

PLAN if `|A_(n xx n)| = Delta, "then" |adj A| = Delta^(A-1)`
`"Here, adj "P_( 3 xx 3) = [{:(1, 4, 4), (2, 1, 7),(1, 1, 3):}]`
`rArr |adj P| = |P|^(2)`
`therefore |adj P| = |{:(1, 4, 4), (2, 1, 7),(1, 1, 3):}| = 1(3-7)-4(6-7) + 4(2-1)`
` =-4 + 4 + 4 = 4 rArr |P| =+-2`
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