your friend says that since -a is the opposite of a, the opposite of a number is always negative, describe and correct the error?
Opposite is the incorrect term to use.
The additive inverse of a = -(a)
If a < 0, then -(-a) = a
(-a) is the negative of (a), and that does not necessarily mean (-a) is a negative number. In the case of (a) being a negative number, then (-a) is positive.
Examples
a = 2
-a = -2
a = -4
-a = 4
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Verified answer
Opposite is the incorrect term to use.
The additive inverse of a = -(a)
If a < 0, then -(-a) = a
(-a) is the negative of (a), and that does not necessarily mean (-a) is a negative number. In the case of (a) being a negative number, then (-a) is positive.
Examples
a = 2
-a = -2
a = -4
-a = 4