What happens to the force between magnetic poles when their pole strength and the distance between them are both doubled

The law states that the force of attraction or repulsion between two magnetic poles is directly proportional to the product of the strengths of the poles and inversely proportional to the square of the distance between them.

Hence the new force F₂ will be given by

$\frac{{\mathrm{F}}_2}{{\mathrm{F}}_1}=\frac{\frac{{\mathrm{m}}_{{\mathrm{A}}_2}\times {\mathrm{m}}_{{\mathrm{B}}_2}}{{\mathrm{d}}_2^2}}{\frac{{\mathrm{m}}_{{\mathrm{A}}_1}\times {\mathrm{m}}_{{\mathrm{B}}_1}}{{\mathrm{d}}_1^2}}=\frac{\frac{2{\mathrm{m}}_{{\mathrm{A}}_1}\times 2{\mathrm{m}}_{{\mathrm{B}}_1}}{2{\mathrm{d}}_1^2}}{\frac{{\mathrm{m}}_{{\mathrm{A}}_1}\times {\mathrm{m}}_{{\mathrm{B}}_1}}{{\mathrm{d}}_1^2}}=1$

$\therefore {\mathrm{F}}_2={\mathrm{F}}_1$