You visited us 1 times! Enjoying our articles? Unlock Full Access!

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

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

either 4 or 2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

None of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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.

Suggest Corrections

Similar questions

A

n

| a d j (a d j A) | = {| A |}^{9}

n

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

A = ⎡ ⎢ ⎣ \begin{matrix} 3 & - 3 & 4 2 & - 3 & 4 0 & - 1 & 1 \end{matrix} ⎤ ⎥ ⎦

a d j (a d j A) = A

a d j (a d j A) = {| A |}^{n - 2} A

A

m \times n

a d j (a d j A)

A

n,

| adj(adj A) | = | A |^{9},

n

Join BYJU'S Learning Program