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.