Question

Let A be a 3 x 3 non-singular matrix such that adj A = adj A^-1, then the value of | A | equals to:
A)1 B) - 1 C) +-1 D) +- 2​

Answer 1

Answer:

Correct option is

A

∣A∣A

Step-by-step explanation:

As A is a non-singular matrix, A is invertible and  A  

−1  =  ∣A∣ adjA

​ ⇒adjA=∣A∣A  −1

=B(say).

Now,

adj(adjA)=adj(B)=∣B∣B  

−1

 

                 =  

∣

∣

∣

​

∣A∣A  

−1

 

∣

∣

∣

​

(∣A∣A  

−1

)  

−1

 

                 =∣A∣  

3

∣A  

−1

∣∣A∣  

−1

(A  

−1

)  

−1

    [using scalar multiple property of determinants]

                 =∣A∣  

3

 

∣A∣

1

​

.  

∣A∣

1

​

A=∣A∣A