If `A=[[alpha, 0], [1, 1]]` and `B=[[1 ,0],[ 5 ,1]],` find the values of `alpha` for which `A^2=B`

Options

A. `1`
B. `2`
C. `-1`
D. No real values

Answer

No real values

Explanation

Given, `A=[[alpha, 0], [1, 1]]` and `B=[[1 ,0],[ 5 ,1]],`

`A^2= B`

`Rightarrow A^2 = [[alpha, 0], [1, 1]][[alpha, 0], [1, 1]] = [[alpha^2, 0], [alpha + 1, 1]]`

`A^2= B`

`Rightarrow [[alpha^2, 0], [alpha + 1, 1]] = [[1 ,0],[ 5 ,1]]`


`Rightarrow alpha^2 =1, alpha +1 =5`



By both equations, value of `alpha` is not matching

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