Here,

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

a₁₁ (co – factor of 3) = (-1)¹⁺¹(2) = (-1)²(2) = 2

a₁₂ (co – factor of -5) = (-1)¹⁺²(-1) = (-1)³(-1) = 1

a₂₁ (co – factor of -1) = (-1)²⁺¹(-5) = (-1)³(-5) = 5

a₂₂ (co – factor of 2) = (-1)²⁺²(3) = (-1)⁴(3) = 3

Now, adj A = Transpose of co-factor Matrix

Calculating A (adj A)

= I

Calculating (adj A)A

= I

Calculating |A|.I

= [3 × 2 – (-1) × (-5)]I

= [6 – (5)] I

= (1)I

= I

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

⇒ A(adj A) = (adj A)A = |A|I

Hence Proved

Ans.