What is the inverse of [-3 5]

[-6 -8]

1/6 *

(8 5)
(6 3)

do you mean

-8-5
6-3

yes, all multiplied by 1/6

See

http://www.wolframalpha.com/input/?i=inverse+{{-3%2C5}%2C{6%2C-8}}

To find the inverse of a 2x2 matrix, you can follow these steps:

1. Start with the given matrix:
A = [-3 5]
[-6 -8]

2. Use the formula for calculating the inverse of a 2x2 matrix:
A^-1 = (1 / det(A)) * adj(A)
where det(A) is the determinant of A and adj(A) is the adjugate of A.

3. Calculate the determinant of A:
det(A) = (-3 * -8) - (5 * -6) = 24 - (-30) = 54

4. Find the adjugate of A:
To find the adjugate of a 2x2 matrix, interchange the positions of the top left and bottom right elements, and change the sign of the top right and bottom left elements.
adj(A) = [-8 5]
[ 6 -3]

5. Plug the determinant and adjugate values into the formula for the inverse:
A^-1 = (1 / 54) * [-8 5]
[ 6 -3]

6. Simplify A^-1:
A^-1 = [(-8 / 54) (5 / 54)]
[( 6 / 54) (-3 / 54)]

So, the inverse of the given matrix is:
A^-1 = [-8/54 5/54]
[ 6/54 -3/54]