Question

Find the adjoint of the following matrix.

`[(2,-3),(3,5)]`

Answer 1

Let A = `[(2,-3),(3,5)]`

Here, a₁₁ = 2, M₁₁ = 5

∴ A₁₁ = (− 1)¹⁺¹(5) = 5

a₁₂ = − 3, M₁₂ = 3

∴ A₁₂ = (− 1)¹⁺²(3) = − 3

a₂₁ = 3, M₂₁ = − 3

∴ A₂₁ = (− 1)²⁺¹(− 3) = 3

a₂₂ = 5, M₂₂ = 2

∴ A₂₂ = (− 1)²⁺² = 2

∴ the co-factor matrix = `[("A"_11,"A"_12),("A"_21,"A"_22)]`

= `[(5,-3),(3,2)]`

∴ adj A = `[(5,3),(-3,2)]`