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:

[∵cos² α + sin² α = 1]

Calculating A (adj A)

[∵cos² α + sin² α = 1]

= I

Calculating (adj A)A

[∵cos² α + sin² α = 1]

= I

Calculating |A|.I

Expanding along C₁, we get

= [0 – 0 + 1(cos² α – (-sin² α))]I

= [cos² α + sin² α] I

= (1)I [∵cos² α + sin² α = 1]

= I

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

⇒ A(adj A) = (adj A)A = |A|I

Hence Proved

Ans.