If A = ((a, 0), (1, 1)) and B = ((1, 0), (5, 1)), and A² = B, the value of a is
A
5
B
-1
C
11
D
No real value of a
Correct Option:
D
Explanation
A = [[a, 0], [1, 1]], so A² = [[a², 0], [a + 1, 1]]. For A² = B = [[1, 0], [5, 1]], we need both a² = 1 and a + 1 = 5. The second condition gives a = 4, which contradicts a² = 1. Hence no real value satisfies both conditions.
