Question

If A is an invertible matrix of order 2, then det (A⁻¹) is equal to ______.

Options

• det (A)

• `1/det (A)`

• 1

• 0

Answer 1

If A is an invertible matrix of order 2, then det (A⁻¹) is equal to `underline(1/det (A))`.

Explanation:

`because` A invertible matrix `=> abs "A" ne 0`

`therefore "AA"^-1 = "I"` and `abs ("AA"^-1) = abs "I" = 1`

`=> abs "A" abs ("A"^-1) = 1` 

`=> abs ("A"^-1) = 1/abs "A"` 

`=> det ("A"^-1) = 1/det("A")`