Question

Find the inverse of the matrices (if it exists).

`[(-1,5),(-3,2)]`

Answer 1

A = `[(-1,5),(-3,2)]`

|A| = `|(-1,5),(-3,2)|`

= −2 + 15

= 13 ≠ 0

Therefore, A⁻¹ exists.

A₁₁ = (−1)¹⁺¹ (2) = 2

A₁₂ = (−1)¹⁺² (−3) = 3

A₂₁ = (−1)²⁺¹ (5) = −5

A₂₂ = (−1)²⁺² (−1) = −1

∴ Adj A = `[(2,3),(-5,-1)] = [(2,-5),(3,-1)]`

A⁻¹ = `1/|A|` (adj A)

= `1/13 [(2,-5),(3,-1)]`