If A is an invertible matrix with |A| = 4, then write the value of det(A^-1).

Write the derivative of sin {cos (x³)} w.r.t x.

Find the direction cosines of a line passing through two points (-2, 4, -5) and (1, 2, 3).

Write the differential equation representing the family of curves y = mx, for some arbitrary constant m.

Prove that the relation R in R, the set of all real numbers, defined as R = {(a, b) : a ≤ b²} is neither reflexive nor transitive.