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 4) = (-1)¹⁺¹(3) = (-1)²(3) = 3

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

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

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

Now, adj A = Transpose of co-factor Matrix

Calculating |A|

= [4 × 3 – 1 × 2]

= (12 – 2)

= 10

Ans.