T:R² → R²
T(x, y) = (y, x), (x,y)∈R²

Eigen Values

• 1 [∵ T(1, 1) = (1, 1) = 1.(1, 1)]
• -1 [∵ T(1, -1) = (-1, 1) = (-1).(1 -1)]

Eigen Vectors

Corresponding to 1: (x, x), x ≠ 0, x ∈ R
Reason: T(1, 1) = (1, 1) = 1.(1, 1)

Corresponding to -1: (-x, x), x ≠ 0, x ∈ R
Reason: T(1, -1) = (-1, 1) = (-1).(1 -1)

Visualization