A real (4 × 4) matrix A satisfies the equation A² = I, where I is a (4 × 4) identity matrix. The positive eigenvalue of A is ________.

In the range: 0.99 - 1.01

Concept :

Eigenvalue of Identity matrix = 1

If λ₁, λ₂, λ₃…. are the eigenvalue of matrix A, then ${\lambda }_2^k,{\lambda }_2^k,{\lambda }_3^k\dots$ are the eigenvalues of A${}^k$

Analysis:

Given: A² = I

So, Eigenvalue of [A²] = Eigenvalue of I = 1

Now,

Eigenvalue (A)² = 1

Eigenvalue (A) = ± 1

So, the positive Eigenvalue of A is +1.