Incorrect. You SPECIFICALLY defined multiplication as $(z_{1_A,} z_{2_A}) \times (z_{1_B}, z_{2_B}) = z_{1_A} z_{2_B} = z_{2_A} z_{1_B} = z_{1_B} z_{2_A} = z_{2_B} z_{1_A}$Incorrect...I did not say

x * 0 = 0

x * 0 = x

therefore

x = 0

I said SPECEFICALLY

(z1for0) * x = 0

(z2for0) * x = x

So if $x=(x,x)$ you have $x\times 0 = x 1 = x 0 = 0 x = 1x $. This was YOUR rule.

If you cannot understand your own rules, how do you expect anyone else to?

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