Solution to Question 19 on Linear Algebra in GATE 2024 Mathematics Examination.

Question 19 from the GATE 2024 examination on Mathematics.
Let A = [
0 2
2 0
]
 and T : M2(C) → M2(C) be the linear transformation given by
T(B) = AB. The characteristic polynomial of T is
(A) X4 − 8X2 + 16
(B) X2 − 4
(C) X2 − 2
(D) X4 − 16