The value of Young’s modulus for a perfectly rigid body is

For perfectly rigid body the condition is that there should not be any elognation $(\mathrm{\Delta L}=0)$ for any value of force So from the formulae we know $\frac{\mathrm{FL}}{\mathrm{A}\cdot \mathrm{\Delta L}}=\mathrm{Y}$
If we put $(\mathrm{\Delta L}=0)$ We get Y as $\infty$