Question

Of A
-8 1
1 4
4 4
4 7. prove that A'=A".
1 -8 4
15​

Answer 1

Answer:

A shortcut is to notice that each element is a power of 7. That is, 70≡1mod7, 71≡1mod7, 72≡4mod7, and 73≡13mod7. Then if a,b∈{1,4,7,13}, there are i,j∈{0,1,2,3} such that 7i≡amod7 and 7j≡bmod7. Then 7i7j≡abmod7 but also 7i7j≡7kmod7 where k∈{0,1,2,3} satisfies i+j≡kmod4. Therefore 7k≡abmod7 and hence ab∈{1,4,7,13}.

Step-by-step explanation:

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