Can two companies cross hold each others 100% shares

Question

Can a company A hold 100% of shares in company B and can this company B have 100% of shares in company A

I couldn't find any information that dissolve this activity.

Answer 1

If this happens, the pair of companies is worthless and might as well not exist.

Proof 1:

• No shares of either company are owned, directly or transitively, by any natural person (human). The ownership chain bounces back and forth endlessly between A and B.
• There is no way for the companies to do anything, because there is no way to legally exercise control or make decisions, which can only be done (directly or transitively) by human owners.

Proof 2:

• Call "external assets" the net assets other than shares of A or B themselves.
• A owns 100% of B, so Value of A = External assets of A + Value of B.
• B owns 100% of A, so Value of B = External assets of B + Value of A.
• By adding the two equations above, External assets of A + External assets of B = 0.
• So A and B do not own any net external assets.
• No value can be created by making the two companies own each other, so the construct is an empty shell.