find the inverse of A, recall that A-1 = 1/det A [d -b]

Question

[ -c a]

Answer 1

You just stated the formula for A^-1, so for your A, just evaluate it according to that formula.
Remember that if A =
a b
c d , then
det A = ad - bc

e.g. suppose A =
4 5
1 2
then det A = 8-5 = 3
and A^-1 =
(1/3)
2 -5
-1 4
=
2/3 -5/3
-1/3 4/3

check by showing:
4 5
1 2
x
2/3 -5/3
-1/3 4/3
=
1 0
0 1