Let M be a 2 $$\times$$ 2 symmetric matrix with integer entries. Then, M is invertible, if

Let M and N be two 3 $$\times$$ 3 matrices such that MN = NM. Further, if M $$\ne$$ N² and M² = N⁴, then

Let $$f:\left( { - {\pi \over 2},{\pi \over 2}} \right) \to R$$ be given by $$f(x) = {[\log (\sec x + \tan x)]^3}$$. Then,

Let a $$\in$$ R and f : R $$\to$$ R be given by f(x) = x⁵ $$-$$ 5x + a. Then,