Question

How do you find the inverse of `A=``((8, 6), (7, 5))`?

Answer 1

`A^-1=((-2 1/2, 3), (3 1/2, -4))`

Explanation:

For `A=((8, 6), (7, 5))`

To find the inverse of a 2x2 matrix: `" "X=((a, b), (c, d))`

1. Find the determinant: `absX = ab-cd`
2. Change the matrix to `((d, -b), (-c, a))`
3. Divide by the determinant

`A^-1 = 1/absA ((5, -6), (-7, 8))`

`absA=8xx5-7xx6 = -2`

`A^-1 = 1/-2((5, -6), (-7, 8))`

`A^-1=((-2 1/2, 3), (3 1/2, -4))`