How does the identity A(I+BA)=(I+AB)A connect the inverses of I+BA and I+AB? Prove that they are both invertible or both singular.
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Originally Posted by alexmahone How does the identity A(I+BA)=(I+AB)A connect the inverses of I+BA and I+AB? Prove that they are both invertible or both singular. Here is an idea, if we know something about if . If is invertible then This would say that is similar to . Since similar Matrices have the same determinant They are both either singular or invertible.
Originally Posted by alexmahone How does the identity A(I+BA)=(I+AB)A connect the inverses of I+BA and I+AB? Prove that they are both invertible or both singular. In the general case, that is singular or not, suppose ( without loss of generality ) singular and invertible, then: This is a contradiction because Fernando Revilla
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