Read each statement below carefully and state,with reasons and examples,if it is true or false:
$A$ scalar quantity is one that
$(a)$ is conserved in a process
$(b)$ can never take negative values
$(c)$ must be dimensionless
$(d)$ does not vary from one point to another in space
$(e)$ has the same value for observers with different orientations of axes.

(E) False: Despite being a scalar quantity,energy is not conserved in inelastic collisions.
$(b)$ False: Despite being a scalar quantity,temperature can take negative values.
$(c)$ False: Total path length is a scalar quantity,yet it has the dimension of length.
$(d)$ False: $A$ scalar quantity such as gravitational potential can vary from one point to another in space.
$(e)$ True: The value of a scalar does not vary for observers with different orientations of axes.