NIMCET 2009 Question Paper with solutions

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Question : 24 of 120

Marks: +1, -0

If

A

is a

3 × 3

matrix with

det(A)=3

, then det

(adj A)

is

3
9
27
6

Solution:

As,

A

adj

A]=|A| I

⇒ |A adj(A)|=\| A|I|

⇒ |A||adj(A)|=|A|^{n}

⇒ \;\; ∣ adj(A||=|A|^{n-1}

where

n

is the order of

A

,

⇒∣

adj

(A) ∣=3^2=9

[ ∵ |A|=3

(given)]

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