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

1 Answer
Feb 13, 2016

Answer:

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))#