Identity element for multiplication is #1#, as any number multiplied by #1# leads to the same number. Multipicative inverse of a number #a#, is a number, which when multiplied with #a# leads to multiplicative identity #1# and it is apparent that multipicative inverse of #a# is #1/a#.
Hence, multiplicative inverse of #-13# is #1/(-13)=-1/13#
and multiplicative inverse of #1/5# is #1/(1/5)=1xx5/1=5#
Additional information - Identity element for addition is #0#, as any number aaded to #0# leads to the same number. Additive inverse of a number #a#, is a number, which when added to #a# leads to additive identity #0# and it is apparent that additive inverse of #a# is #-a#.
Also observe that while in additive inverse, sign changes but number does not change; in multiplicative inverse, it remains same but numerator and denominator, change their places.
Observe that if we have a whole number for example #-13#, we just write it as #-13/1# (note that #-13# and #-13/1# are same) and then change places of numerator and denominator and multilicative inverse is #-1/13#. And if numerator is #1#, say in #1/5#, then we change it into #5/1# and make it #5#.
