Let A = [(1, 0, 0), (1, 0, 1), (0, 1, 0)] satisfies An = An–2 + A2 – I for n ≥ 3 And trace of a square matrix X is equal to the sum of elements in its principal diagonal.
Further consider a matrix U3×3 with its column as U1, U2, U3 such that A50 U1 = [(1, 25, 25)] , A50 U2 = [(0, 1, 0], A50 U3 = [0, 0, 1]
Then answer the following questions.
1. The value of |A50| equals
(A) 0
(B) 1
(C) –1
(D) 25
2. Trace of A50 equals
(A) 0
(B) 1
(C) 2
(D) 3
3. The value of |U| equals
(A) 0
(B) 1
(C) 2
(D) –1