Let F be a field, and suppose a EF, a *0. Prove that a has a unique multiplicative inverse.
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To do this, we're going to use the order of operations (PEMDAS):
P - Parentheses
E - Exponents
M - Multiplication
D - Division
A - Addition
S - Subtraction
First let's do parentheses, there isn't anythig in parentheses we need to simplify, so we can skip this step.
Next let's look for exponents. I see we have a so let's replace that with
:
Now let's look for multiplcation. We know that things that are right next to eachother in parentheses represent multiplcation, so let's simply this more:
And now we're left with a simple problem we know how to solve.
Answer:
Hope this helps!