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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

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The correct Answer is:
A, D
Given, `"adj " P = [[1,4,4],[2,1,7],[1,1,3]]`
`rArr abs(adj P )= abs((1,4,4),(2,1,7),(1,1,3))`
`= 1(-4) - 4 (-1) + 4 (1) = 4`
`rArr abs(P)^(3-1) = 4`
`rArr abs(P) = pm 2`
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