Question

How do you find the inverse of `A=``((3, 4), (5, 6))`?

Answer 1

Use the general formula for the inverse of a `2xx2` matrix to find:

`((3,4),(5,6))^(-1) = ((-3,2),(5/2,-3/2))`

Explanation:

The inverse of a `2xx2` matrix is given by the formula:

`((a, b),(c, d))^(-1) = 1/abs((a, b),(c,d)) ((d, -b),(-c, a))`

where the determinant is given by the formula:

`abs((a, b),(c,d)) = ad-bc`

In our case `((a, b),(c, d)) = ((3,4),(5,6))` and we find:

`abs((a,b),(c,d)) = abs((3,4),(5,6)) = (3*6)-(4*5) = -2`

So:

`((3,4),(5,6))^(-1) = 1/(-2) ((6,-4),(-5,3))=((-3,2),(5/2,-3/2))`