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If the matrices AB, A, and B are all equal, then what is the value of B squared?

1. B
2. A
3. I
4. O

Correct answer: B

Solution

Since AB = A = B, we can substitute B for A in the equation AB = B, leading to B² = B. This indicates that B is idempotent, confirming that the value of B squared is B itself.

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