JEE Main 2003 Mathematics question on Matrices and Determinants
If A=[α101] and B=[1501] then value of α for which A2=B, is
A.
1
B.
-1
C.
4
D.
no real values
Show answer and solution
Correct option: D
Solution
Computing A² directly: A² = [[α², 0], [α+1, 1]]. Setting A² = B gives α² = 1 and α+1 = 5. From α² = 1, α = ±1, but α+1 = 5 requires α = 4. These two conditions are contradictory, so no real value of α satisfies both simultaneously.
[AIEEE 2003]
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