Determine the veracity of the inequality

Question

Prove if is true or false this statement:

If $q > 0$ , is always $q^{-1} > 0$ ?

Edited:

I tried to elevate both sides to pow of $-1$, but the inequality is indeterminate, due to $0 ^ -1$

Answer 1

The reciprocal of q is equal to 1 divided by q. 1 is positive and q is known to be positive. Dividing a positive number by a positive number always yields a positive number. Thus the statement is true.