線性代數證明題

Definition: If a is a number in Zm, then a number in Zn, denoted a^(-1) is called the multiplicative inverse of a if a*a^(-1)=1(mod m),

For example, when m=26
a a^(-1)
1, 1 >>1*1=1=26*0+1
3, 9 >>3*9=27=26*1+1
5, 21 >>5*21=105=26*4+1
7, 15 >>7*15=105=26*4+1
9, 3 >>9*3=27=26*1+1
11, 19
15, 7
17, 23
19, 11
21, 5
23, 17
25, 25

Proof: given invertible integers a,b in Zm where a+b=m, then a^(-1)+b^(-1)=m

For example,m=26, a=3, b=23, a^(-1)=9, b^(-1)=3.a+b=a^(-1)+b^(-1)=26=m



請問有人會解嗎,想了好幾天總是卡住.
若題目有哪裡表達的不清楚的請告訴我,我會再試著說的明白一點,謝謝