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Ah I see now. Actually 2 is that AX=O only has the <em>trivial</em> solution. An old textbook I have also lists two more after 4 and before 5:
A is expressible as a product of elementary matrices, and
AX=B is consistent for every n by 1 matrix B.
In fact, that theorem can also be extended to at least 17 parts after you include things about linear transformations, spanning, basis, and rank/nullity. Pretty cool.
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