Computer Sciences > GATE 2025 SET-2 > Linear Algebra
If 
then which ONE of the following is A8?
then which ONE of the following is A8?A
B
C
D
Correct : c
The correct answer is Option C — the Identity matrix I.
The matrix A = [[0,1],[1,0]] is a permutation matrix that swaps the two rows when multiplied.
A2 = A × A = [[0,1],[1,0]] × [[0,1],[1,0]] = [[1,0],[0,1]] = I
So A2 = I. Therefore:
A8 = (A2)4 = I4 = I
Any even power of A gives the identity matrix. Any odd power gives A itself. Since 8 is even, A8 = I.
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