Question

multiplicative inverse of -13/7*14/26​

Answer 1

The multiplicative inverse of -13/7 14/26 is -1

Answer 2

Step-by-step explanation:

What is the multiplicative inverse of 7 modulo 11?

Is this correct:

7=11(0)+77=11(0)+7

11=7(1)+411=7(1)+4

7=4(1)+37=4(1)+3

4=3(1)+14=3(1)+1

We then take 3 equations:

4=11+7(−1)4=11+7(−1)

3=7+4(−1)3=7+4(−1)

1=4+3(−1)1=4+3(−1)

We then use the 3 equations and replace them in each other like so:

3 and 2

4+(7+4(−1))(−1)=14+(7+4(−1))(−1)=1

which gives us

(2)4+7(−1)=1(2)4+7(−1)=1

1 and our equation above

(2)(11+7(−1))+7(−1)=1(2)(11+7(−1))+7(−1)=1

This will then simplify to:

11(2)+7(−3)=111(2)+7(−3)=1

We then can say (we know that 11−(−3)=1411−(−3)=14)

11(2)+7(14)=1mod1111(2)+7(14)=1mod11

And we know that 11(2