Question 323071
The opposite of a would be -a.


The reciprocal of a would be 1/a.


The question says to find all values of a such that 
-a=1/a


Multiply both sides by a:
-a*a=(1/a)*a
-a^2 =1


Add a^2 to each side:
0=a^2+1


Or, rewrite this as a^2=-1.


There are NO REAL VALUES of a for which a^2=-1.  NO SOLUTION!!


Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus