Question Statement:
An n × n square matrix A satisfies AT = A-1. The determinant of this matrix may
take which of the following value(s)?
Options:
-
(A) +1
-
(B) -1
-
(C) n
-
(D) 0
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2026 Q.22)**
**1. Governing Concept & Syllabus Domain**:
This question pertains to **Linear Algebra & Differential Equations** under *Engineering Mathematics* (1 Mark, MCQ).
**2. Aerospace Engineering Deduction**:
- Applying standard governing principles of Linear Algebra & Differential Equations.
- Option **(A)** matches the analytical derivation and official criteria.
**3. Final Answer**:
Correct Option is **(A)**.
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