further Mathematics
posted by James .
Let A=(cosA sinA)
(sinA cosA)
show that
A^2=(cos2A sin2A)
(sin2A cos2A)

A^2 = (cosAsinA)^2 (sinAcosA)^2
= (cos^2A2sinAcosA+sin^2A)(sin^2Acos^2A)
= (12sinAcosA)(1/4)(2sinAcosA)^2
= (1/4)(1sin2A)(sin2A)(sin2A)
Hmmm. What if A = pi/4?
(1/√2 + 1/√2)(1/√2 * 1/√2) =? (0)(0)
1/√2 =? 0
Nope. I don't think it's true. Typo?