State the reason why the Relation R = {(a, b) : a ≤ b²} on the set R of real numbers is not reflexive.

State the reason for the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} not to be transitive.
Show that a function f : R → R given by f(x) =ax + b,a, b ∈ R, a ≠ 0 is a bijective.
If the determinant of matrix A of order 3 × 3 is of value 4, write the value of |3A|.
In the interval , find the value of x for which that matrix is singular.