Given two $$ n imes n $$ invertible matrices $$ A $$ and $$ B $$ such that $$ (A-B)(B+A)=A^{2}-B^{2} $$. Which of the following statement is correct? $$ B=A B A^{-1} B $$ $$ A $$ is the inverses matrix of $$ B $$ $$ B=B A B A^{-1} $$ None of the given options $$ B=A^{-1} B A $$

Question

Given two $$ n 	imes n $$ invertible matrices $$ A $$ and $$ B $$ such that $$ (A-B)(B+A)=A^{2}-B^{2} $$. Which of the following statement is correct? $$ B=A B A^{-1} B $$ $$ A $$ is the inverses matrix of $$ B $$ $$ B=B A B A^{-1} $$ None of the given options $$ B=A^{-1} B A $$

Ross Romero · Accepted Answer

The correct statement is $$ B = A^{-1}BA $$.

Given two \( n \times n \) invertible matrices \( A \) and \( B \) such that \( (A-B)(B+A)=A^{2}-B^{2} \). Which of the following statement is correct? \( B=A B A^{-1} B \) \( A \) is the inverses matrix of \( B \) \( B=B A B A^{-1} \) None of the given options \( B=A^{-1} B A \)

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Given two \( n \times n \) invertible matrices \( A \) and \( B \) such that \( (A-B)(B+A)=A^{2}-B^{2} \). Which of the following statement is correct? \( B=A B A^{-1} B \) \( A \) is the inverses matrix of \( B \) \( B=B A B A^{-1} \) None of the given options \( B=A^{-1} B A \)

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Solución paso a paso

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