Answer with Step-by-step explanation:
Let F be a field .Suppose and
We have to prove that a has unique multiplicative inverse.
Suppose a has two inverses b and c
Then, where 1 =Multiplicative identity
(cancel a on both sides)
Hence, a has unique multiplicative inverse.
Answer:
187
Step-by-step explanation:
A number m is such that when it is divided by 30, 36 and 45 the remainder is always 7.
We should first find the LCM of 30, 36 and 45
We get that the LCM of the three numbers is 280 (working attached).
So now;
= 6
= 5
= 4
But we need a number that leaves a remainder of 7 so we add 7 to 180 to get; 180 + 7 = 187.
