F'01 = A0αA1βFαβ = A00A10F00 + A00A11F01 + A01A10F10 + A01A11F11. <= Terms vanish due to 0’s in A.
F'01 = A00A11F01 + A01A10F10 <= Terms vanish due to 0’s in F.
F'01 = C2F01 + S2F10 <= Definition of A
F'01 = C2F01 − S2F01 <= Anti-symmetry of F
F'01 = (C2 − S2)F01 = F01 = −x <= (cosh x)2 − (sinh x)2 = 1.

If j = 2 or j = 3 then
F'0j = A0αAjβFαβ = A0αAj2Fα2 + A0αAj3Fα3 <= varying β: Terms vanish due to 0’s in A.
F'0j = A00Aj2F02 + A00Aj3F03 + A01Aj2F12 + A01Aj3F13 <= varying α: Terms vanish due to 0’s in A.
F'02 = A00A22F02 + A01A22F12 <= Terms vanish due to 0’s in A.
F'02 = CF02 + SF12 <= A00 = C & A22 = 1 & A01 = S .
F'02 = —Cy <= F12 = 0

junk
but Aj2F02 = F0j