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Question 16.6.3: Find the inverse of the n × n matrix A if A − A² = I....

Find the inverse of the n × n matrix A if A − A² = I.

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The matrix equation A − A² = I yields A(I − A) = I. But then it follows from (16.6.4) that A has the inverse A^{−1} = I − A.

AX = I ⇒ X = A^{−1}        (16.6.4)

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