find matrix A...?

Question

let A be an invertible matrix, and suppose that the inverse of 5A is the following:

3 -4
5 -7

(a 2x2 matrix)

what is A??

Answer 1

The inverse of 5A has determinant -1, so

- 5A =

|-7, 4|
|-5, 3|,

(by the standard inversion formula) and so

A =

|7/5, -4/5|
|1, -3/5|