Question

Find the adjoint of the following matrices : `[(2, -3),(3, 5)]`

Answer 1

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

Here,
a₁₁ = 2
∴ M₁₁ = 5 and A₁₁ = (– 1)¹⁺¹ (5) = 5
a₁₂ = – 3

∴ M₁₂ = 3 and A₁₂ = (– 1)¹⁺² (3) = – 3
a₂₁ = 3

∴ M₂₁ = – 3 and A₂₁ = (– 1)²⁺¹ (– 3) = 3
a₂₂ = 5
∴ M₂₂ = 2 and A₂₂ = (– 1)²⁺² (2) = 2
∴ The matrix of the co-factors is

[A_ij]_2x2 = `[("A"_11, "A"_12),("A"_21, "A"_22)] = [(5, -3),(3, 2)]`

Now, adj A = `["A"_"ij"]_(2xx2)^"T" = [(5, 3),(-3, 2)]`.