Find the adjoint of the given matrix and verify in each case that A. (adj A) = (adj A) =m |A|.I.

Here,

Now, we have to find adj A and for that we have to find co-factors:

Calculating A (adj A)

= -132I

Calculating (adj A)A

= -132I

Calculating |A|.I

Expanding along C₁, we get

= [4(0 – 42) – (1){45 – 21} + 2(30 – 0 )]I

= [4(-42) – 1(24) + 2(30)] I

= (-168 – 24 + 60)I

= -132I

Thus, A(adj A) = (adj A)A = |A|I = -132I

⇒ A(adj A) = (adj A)A = |A|I

Hence Proved

Ans.