Here,

We have to find A^-1 and

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

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

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

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

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

Now, adj A = Transpose of co-factor Matrix

Calculating |A|

= [a × d – c × b]

= ad – bc

Ans.