If A is a square matrix of order n such that - adj adj A - A -9- then the value of n can beA- 4B- 2C- either 4 or 2D- None of these

The correct option is A 4 We know that for a square matrix of order n, |adj A| =|A|^n 1 ⇒ |adj (adj A)|=|adj A|^n 1=|A|^(n 1)^2=|A|^9 ⇒ (n 1)^2=9 ⇒ n^2 2n 8=0 ...

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Standard XII

Mathematics

Cramer's Rule

If A is a squ...

Question

If A is a square matrix of order n such that |adj (adj A)| $= | A |^{9}$ , then the value of n can be

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either 4 or 2

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None of these

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Solution

The correct option is A
4

We know that for a square matrix of order n, |adj A| $= | A |^{n - 1}$
$\Rightarrow | a d j (a d j A) | = | a d j A |^{n - 1} = | A |^{(n - 1)^{2}} = | A |^{9} \Rightarrow (n - 1)^{2} = 9 \Rightarrow n^{2} - 2 n - 8 = 0$
$\Rightarrow$ n = 4 as n =-2 is not possible.

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If A is a square matrix of order n such that |adj (adj A)|=|A|9, then the value of n can be

The correct option is A 4 We know that for a square matrix of order n, |adj A| =|A|n−1 ⇒ |adj (adj A)|=|adj A|n−1=|A|(n−1)2=|A|9⇒ (n−1)2=9⇒n2−2n−8=0 ⇒ n = 4 as n =-2 is not possible.

If A is a square matrix of order n such that |adj (adj A)| $= | A |^{9}$ , then the value of n can be

The correct option is A
4

We know that for a square matrix of order n, |adj A| $= | A |^{n - 1}$
$\Rightarrow | a d j (a d j A) | = | a d j A |^{n - 1} = | A |^{(n - 1)^{2}} = | A |^{9} \Rightarrow (n - 1)^{2} = 9 \Rightarrow n^{2} - 2 n - 8 = 0$
$\Rightarrow$ n = 4 as n =-2 is not possible.