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)

= -2I

Calculating (adj A)A

= -2I

Calculating |A|.I

Expanding along C₁, we get

= [0(2 – 3) – (1){1 – 2} + 3(3 – 4)]I

= [0 – 1(-1) + 3(-1)] I

= (1 – 3)I

= -2I

Thus, A(adj A) = (adj A)A = |A|I = -2I

⇒ A(adj A) = (adj A)A = |A|I

Hence Proved

Ans.