Rowe Cook

01/23/2024 · Elementary School

Assume that \( \operatorname{det}(A), \operatorname{det}(B) \) and \( \operatorname{det}(A+B) \) are all non zero values. Which of the followir statement(s) is/are correct? \( A(A+B) B^{-1}=A^{-1}+B^{-1} \) \( A^{-1}(A+B) B^{-1}-\left(A^{-1}+B^{-1}\right)=O \), where \( O \) is the zero matrix with zero entries everywhere. \( A(A+B) B\left(A^{-1}+B^{-1}\right)=I_{n} \), where \( I_{n} \) is the \( n \times n \) identity matrix. None of the given option \( A^{-1}(A+B) B^{-1}-\left(A^{-1}+B^{-1}\right)=I_{n} \) where \( I_{n} \) is the \( n \times n \) identity matrix.