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Question 133

If A, B are two matrices such that AB = A, BA = B, then $$A^2 + B^2$$ =

Solution

AB=A and BA=B

Hence A and B are identity matrices

The square of an identity matrix is the matrix itself

Hence $$A^2=A\ and\ B^2=B$$

So $$A^2+B^2=A+B$$

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