GATE 2014 EC (EC1) – Question 14
A real 4 × 4 matrix A satisfies $A^2=I$, where I is the identity. Find the positive eigenvalue of A.
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Correct answer: 0.99 to 1.01
Explanation
If Av=λv with v nonzero, applying A again gives A²v=λ²v=v. Hence λ²=1 and every eigenvalue is either1or−1. Any positive eigenvalue must therefore be **1**. The identity does not by itself guarantee a positive eigenvalue exists; A=−I is a counterexample.