A

Step 1: Understand the concept of modulus of rigidity, which is a measure of a material's ability to withstand deformation under shear stress.
Step 2: The modulus of rigidity is defined as the ratio of shear stress to shear strain. Its formula is given by: $$ G = \frac{\tau}{\gamma} $$ where $G$ is the modulus of rigidity, $\tau$ is the shear stress (in N/m² or Pascals), and $\gamma$ is the shear strain (dimensionless).
Step 3: Since shear stress has units of N/m² and shear strain is dimensionless, the units of modulus of rigidity are also in N/m².
Step 4: The units N/m² can also be expressed as Pascal (Pa). Therefore, the units of modulus of rigidity are Pascal (Pa).
Conclusion: The correct answer is Option A (N/m²).