Question

If A = `[(-4, -3, -3),(1, 0, 1),(4, 4, 3)]`, find adj (A).

Answer 1

A₁₁ = (–1)¹⁺¹ M₁₁ = `1|(0, 1),(4, 3)|` = 1(0 – 4) = – 4

A₁₂ = (–1)¹⁺² M₁₂ = `(-1)|(1, 1),(4, 3)|` = (–1)(3 – 4) = (–1)(–1) = 1

A₁₃ = (–1)¹⁺³ M₁₃ = `1|(1, 0),(4, 4)|` = 1(4 – 0) = (1)(4) = 4

A₂₁ = (–1)²⁺¹ M₂₁ = `(-1)|(-3, -3),(4, 3)|` = (–1)(– 9 + 12) = (–1)(3) = – 3

A₂₂ = (–1)²⁺² M₂₂ = `1|(-4, -3),(4, 3)|` = 1(–12 + 12) = 1(0) = 0

A₂₃ = (–1)²⁺³ M₂₃ = `(-1)|(-4, -3),(4, 4)|` = (–1)(–16 + 12) = (–1)(–4) = 4

A₃₁ = (–1)³⁺¹ M₃₁ = `1|(-3, -3),(0, 1)|` = 1(– 3 – 0) = – 3

A₃₂ = (–1)³⁺² M₃₂ = `(-1)|(-4, -3),(1, 1)|` = (–1)(– 4 + 3) = (–1)(–1) = 1

A₃₃ = (–1)³⁺³ M₃₃ = `1|(-4, -3),(1, 0)|` = 1(0 + 3) = (1)(3) = 3

adj (A) = `[("A"_11, "A"_12, "A"_13),("A"_21, "A"_22, "A"_23),("A"_31, "A"_32, "A"_33)]``

= `[(-4, 1, 4),(-3, 0, 4),(-3, 1, 3)]`

= `[(-4, -3, -3),(1, 0, 1),(4, 4, 3)]`