Question

If `A =[[2,-3],[3,5]]` then find A^-1 by adjoint method. 

Answer 1

Given `A =[[2,-3],[3,5]]`

`therefore |A| =|[2,-3],[3,5]|=10+9=19ne0`

∴A^-1 exist

A₁₁ = (-1)¹⁺¹.M₁₁ = 5

A₁₂ = (-1)¹⁺².M₁₂ = -3

A₂₁ = (-1)²⁺¹.M₂₁ = -(-3) = 3

A₂₂ = (-1)²⁺².M₂₂ = 2

Hence, matrix of the co-factors is