asymmetry in positive and negative numbers

Why is -1 * -1 = +1 and +1 * +1 = +1 ?
Why is -1 * +1 = -1 ?

Why are there these asymmetries in such elementary ideas? I don't
remember ever being exposed to an explanation and would be grateful for
any comments or links to the history of these operations.

This is a mathematics question but - I am new to groups- I don't seem
to be able to find an apparently serious maths group in Google or
Usenet.

.

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