(a) A ; (b) A

For a given strain, the stress for material $A$ is more than it is for material $B ,$ as shown in the two graphs.

Young's modulus $=\frac{\text { stress }}{\text { strain }}$

For a given strain, if the stress for a material is more, then Young's modulus is also greater for that material. Therefore, Young's modulus for material $A$ is greater than it is for material $B.$

The amount of stress required for fracturing a material, corresponding to its fracture point, gives the strength of that material. Fracture point is the extreme point in a stress-strain curve. It can be observed that material $A$ can withstand more strain than material $B$.

Hence, material $A$ is stronger than material $B$.