Question: Let A,B be n n matrices such that BA + B2 = I - BA2, where I is the n n identity matrix.

Let A,B be n × n matrices such that BA + B2 = I - BA2, where I is the n × n identity matrix. Which of the following is always true? 


1. A is nonsingular

2. B is nonsingular

3. A+B is nonsingular

4. AB is nonsingular

5. A/B is nonsingular

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