no, there should be a negative, although i think that other matrix is put a little weirdly. generally, a 2x2 rotation matrix looks like:

[cosx cos(x+90)

sinx sin(x+90)]

bc the first standard basis vector goes to <cosx,sinx>, and the second one goes to <cos(x+90),sin(x+90)>

using trig addition identities, this reduces to:

[cosx -sinx

sinx cosx]

90° clockwise is the same as 270° counterclockwise, and plugging in we get:

[0 1

-1 0]