Question

If `A = [{:(alpha, 0), (1, 1):}] " and " B = [{:(1, 0), (5, 1):}]` then value of `alpha` for which `A^(2) = B`, is
A. 1
B. -1
C. 4
D. no real values

Answer 1

Correct Answer - D
Given, `A = [{:(alpha, 0), (1, 1):}], B = [{:(1, 0), (5, 1):}]`
`rArr A^(2) = [{:(alpha, 0), (1, 1):}] [{:(alpha, 0), (1, 1):}] = [{:(alpha^(2), 0), (alpha+1, 1):}]`
Also given, `A^(2) = B`
`rArr [{:(alpha^(2), 0), (alpha+1, 1):}] = [{:(1, 0), (5, 1):}]`
`rArr alpha^(2) = 1 " and " alpha + 1 =5`
Which is not possible at the same time.
`therefore` No real values of `alpha` exists.