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Let A=(fig 1), prove that (i) (adj A)^-1 = adj(A)^-1 (ii) (A^-1)^-1=A
Let A=(fig 1), prove that (i) (adj A)^-1 = adj(A)^-1 (ii) (A^-1)^-1=A
CBSE | Class 12 | Determinants | Maths | Miscellaneous | NCERT
Let A=(fig 1), prove that (i) (adj A)^-1 = adj(A)^-1 (ii) (A^-1)^-1=A

Given: Matrix A = 

 

  = 

Therefore,  exists.

  and 

and 

 adj. A =  = B (say)

  =            ………(i)

 

=  = 

Therefore,  exists.

  and 

and 

 adj. B =  = 

 

= 

=  ….(ii)

Now to find  (say), where

C = 

= 

C = 

C =  =  =

Therefore,  exists.

  and 

and 

 adj. A = 

=  ……….(iii)

Again 

= 

=  = A (given)

(i) 

 = 

[From eq. (ii) and (iii)]

(ii) 

  = 

i

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