Question 413472
It could happen. If {{{x*x = x}}}, then {{{x^2 - x = 0}}} --> {{{x(x-1) = 0}}}, x = 0 or 1.


However you stated the subject was "trigonometry." You may be referring to the dot product of two vectors A and B. If X is a vector, then we want the dot product equal to the original vector in direction and magnitude, hence


{{{abs(X)*abs(X)*cos(theta) = X}}}, where {{{theta}}} is the angle in between. Since we're multiplying the same vector, {{{theta = 0}}} and {{{cos(theta) = 1}}}. It is indeed possible to have a vector such that {{{abs(X)*abs(X) = X}}}, which happens when X = 1i+0j or X = 0.