Question

Let A be a non-singular square matrix of order 3×3. Then |adj(adjA)| is equal to
|A|^16
|A|^8
|A|^2
|A|^4

Answer 1

Answer:

We know that

AadjA=∣A∣I

n

⇒∣AadjA∣=∣∣A∣I

n

∣

⇒∣A∣∣adjA∣=∣A∣

n

∣I

n

∣ (∵∣AB∣=∣A∣∣B∣;∣kA∣=k

n

∣A∣)

∣A∣∣adjA∣=∣A∣

n

∣I

n

∣ (Determinant of identity matrix is 1)

Dividing by ∣A∣, we get

⇒∣adjA∣=∣A∣

n−1

(Since, A is non-singular i.e.∣A∣



=0)

So, if A is a square matrix of order 3,

∣adjA∣=∣A∣

2