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in Zp, where a does not equal 0, that [a][x] = [a][y] is the same as [x] = [y].

This was a question on a test I just finished. Just curious how wrong my answer is. So I sort of ignored the congruence class part. I just said:

* [a]^-1 represents the inverse of [a] *

[a][x] = [a][y]

[a]^-1[a][x] = [a][y][a]^-1 (by associative law)

[1][x] = [1][y] (by the law of inverses)

[x] = [y] (since 1 is the identity element under multiplication in congruence classes).

so yea... did i do anything right?

thanks for the help in advance

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# Homework Help: Proof of cancellation law

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