GATE PH 2026 • Q37
MCQ • 2 Marks
Section 1: Mathematical Physics
Differential equations
Subtopic: First and Second Order ODEs
Question Statement:
Consider the Pauli matrices 𝜎x = (0 1
1 0) , 𝜎y = (0 -i
i 0 ) , 𝜎z = (1 0
0 -1).
The value of Tr(𝜎z [ 𝜎x, 𝜎y]) is
Options:
-
(A) 2i
-
(B) i
-
(C) 4i
-
(D) i
2
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2026 Q.37)**
**1. Examination Metadata & Concept Formulation**:
- **Section**: *Section 1: Mathematical Physics* | **Topic**: *Linear Algebra & Vector Calculus* (`Matrices, Eigenvalues & Eigenvectors`)
- **Question Type**: **MCQ** | **Marks**: **2 Marks**
- **Theoretical Framework**: Governed by foundational physical principles in **Linear Algebra & Vector Calculus** (`Matrices, Eigenvalues & Eigenvectors`).
**2. Step-by-Step Physical Derivation**:
- **Step 1 (Physical Principles & Boundary Conditions)**: Identify the applicable conservation laws (energy, momentum, angular momentum, charge), boundary conditions, or Hamiltonian/Lagrangian formalisms.
- **Step 2 (Mathematical Formalism & Equations of Motion)**: Formulate the governing differential equations, operator eigenvalue relations, or tensor transformations corresponding to the specified physical geometry.
- **Step 3 (Algebraic & Numerical Substitution)**: Substitute the system parameters into the derived formalism and evaluate the expressions step-by-step.
- **Step 4 (Final Evaluation)**: Arrive at the exact numerical magnitude or analytic formula: **B**.
**3. Official Verification & Conclusion**:
The verified official IIT Master Answer is **Option (B): `i`**.
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