Is A^B positive?

(1) B^A is positive

(2) B is negative

Hi, i could not find this question with the search function:

(1)

B = negative, then A even and positive

B = positive, then A even or odd and positive or negative

-->not sufficient

(2)

B = negative and if A positive, then A^B positive. But if A negative, then A^B negative

--> not sufficient

(1)+(2)

B = negative

A = must be even and positive

--> If A positive, then A^B is positive

Do i think wrong here? Cause the explanation states: Statements (1) and (2) combined are insufficient. Consider \(B = -2\) , \(A = 2\) (the answer is "yes") and \(B = -1\) , \(A = -2\) (the answer is "no").