Question

Find the inverse of the matrices `[(-1, 5),(-3, 2)]`

Options

• `1/13`

• `- 1/13[(2, -5),(3, -1)]`

• `1/13[(2, -5),(3, -1)]`

• `13[(2, -5),(3, -1)]`

Answer 1

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

Explanation:

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

Here, |A| = – 2 + 15 = 13

Since cofactor of `a_(ij)` is `A_11 = (-1)^(i + j) M_i`

A₁₁ = 2, A₁₂ = 3, A₂₁ = – 5, A₂₂ = – 1

∴ Adj A = `[(2, -5),(3, -1)]`

`A^-1 = 1/|A| adj A = 1/13[(2, -5),(3, -1)]`