Help interpreting a question ... I don't understand what this question is asking me to do.

Here is the question:
(a) Find the inverse of the rotation matrix R_theta=(row1 cos(theta), -sin(theta) row2 sin(theta), cos(theta)) Where theta is a fixed angle.

(b) Use your result to solve the system
x=acos(theta)-bsin(theta)
y=asin(theta)+bcos(theta)
for a and b in terms of x and y.

(c) Prove that, for any real number a, and 0
I got part a: Rinverse_theta=( row1(cos(theta), sin(theta) row2(-sin(theta), cos(theta))

Now i'm unsure of what it is asking me to do in part b.... any help interpreting the question would be greatly appreciated.

Part b, as requested:

Consider the matrix equivalent to the equations in (b). This equation can be written as:

[x,y] = R_theta * [a,b]

Rinverse_theta [x,y] = Rinverse_theta * R_theta * [a,b]

Rinverse_theta [x,y] = 1 * [a,b]

[a,b] = Rinverse_theta [x,y]

Now turn this back into the two eqns for a and b in terms of x and y using the Rinverse_theta matrix you calculated.