In the usual basis (î ĵ k̂), construct the matrix T_x representing a rotation through angle θ about the x axis, and the matrix T_y representing a rotation through angle θ about the y axis. Suppose now we change bases, to î '= ĵ, ĵ' = -î, k̂' = k̂. Construct the matrix S that effects this change of basis, and check that ST_xS^-1 and ST_yS^-1 are what you would expect.