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

Question

Philoid · Accepted Answer

Here,

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

Calculating A (adj A)

= I

Calculating (adj A)A

= I

Calculating |A|.I

Expanding along C₁, we get

= [3(12 – 10) – (-15){-2 – (-2)} + 5(5 – 6)]I

= [3(2) + 15(0) + 5(-1)] I

= (6 – 5)I

= I

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

⇒ A(adj A) = (adj A)A = |A|I

Hence Proved

Ans.