Question

Find the cofactors of the elements of the matrix `[(2, -3),(3, 5)]`.

Answer 1

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

Here, a₁₁ = 2, M₁₁ = 5

∴ A₁₁ = (–1)^{1 + 1} M₁₁ = 1(5) = 5

a₁₂ = –3, M₁₂ = 3

∴ A₁₂ = (–1)^{1 + 2} M₁₂ = –1(3) = –3

a₂₁ = 3, M₂₁ = –3

∴ A₂₁ = (–1)^{2 + 1} M₂₁ = –1(–3) = 3

a₂₂ = 5, M₂₂ = 2

∴ A₂₂ = (–1)^{2 + 2} M₂₂ = 1(2) = 2.

Hence, A₁₁ = 5, A₁₂ = –3, A₂₁ = 3, A₂₂ = 2.