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1. Spivak 4th Edition Problem 1 (i) Chapter 1

If ax = a for some a not equal to 0, then x = 1.

2. P7 where a*a^-1=a^-1*a=1

3. Using P7

Then (x^-1)ax=a

then (X^-1 * x)a=a

then 1*a=a

then x=1

Am I approaching this correct or am I supposed to prove P7 as well or prove this a whole different way. Thank you in advance.

If ax = a for some a not equal to 0, then x = 1.

2. P7 where a*a^-1=a^-1*a=1

3. Using P7

Then (x^-1)ax=a

then (X^-1 * x)a=a

then 1*a=a

then x=1

Am I approaching this correct or am I supposed to prove P7 as well or prove this a whole different way. Thank you in advance.

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