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Is this true?

AB = I ⇒ BA = I for all matrices

No — it is false.

The counterexample

This one comes with the Notes pack.

See pricing

85 counterexamples are free — including most of the ones Part C leans on hardest.

The kind of mistake this is

Execution slip

The idea was right. The computation was not.

Drill statements like this
linear algebra

Others that fail the same way

From Determinants and Matrix Tricks › Determinants, trace, block matrices, rank inequalities

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