Question

11. If A and B are two invertible n x n square matrices, then AB is also invertible and (AB)$^{-1}$ = A$^{-1}$B$^{-1}$. AB is also invertible and (AB)$^{-1}$ = B$^{-1}$A$^{-1}$. A + B is also invertible and (A + B)$^{-1}$ = A$^{-1}$ + B$^{-1}$. A + B is also invertible and (A + B)$^{-1}$ = A$^{-1}$ - B$^{-1}$.

          11. If A and B are two invertible n x n square matrices, then
AB is also invertible and (AB)$^{-1}$ = A$^{-1}$B$^{-1}$.
AB is also invertible and (AB)$^{-1}$ = B$^{-1}$A$^{-1}$.
A + B is also invertible and (A + B)$^{-1}$ = A$^{-1}$ + B$^{-1}$.
A + B is also invertible and (A + B)$^{-1}$ = A$^{-1}$ - B$^{-1}$.

11. If A and B are two invertible n x n square matrices, then
AB is also invertible and (AB)^-1 = A^-1B^-1.
AB is also invertible and (AB)^-1 = B^-1A^-1.
A + B is also invertible and (A + B)^-1 = A^-1 + B^-1.
A + B is also invertible and (A + B)^-1 = A^-1 - B^-1.

Added by Patricia J.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Suzanne W.

01/07/2022

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We need to determine the correct statement about the invertibility of AB and A+B, and their respective inverses. Show more…

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If A and B are two invertible n imes n square matrices, then AB is also invertible and (AB)^(-1)=A^(-1)B^(-1). ( AB is also invertible and (AB)^(-1)=B^(-1)A^(-1). (C) A+B is also invertible and (A+B)^(-1)=A^(-1)+B^(-1). (b) A+B is also invertible and (A+B)^(-1)=A^(-1)-B^(-1). 11. If A and B are two invertible n n square matrices, then AB is also invertible and (AB)-1 = A-1B-1 AB is also invertible and (AB)-1 = B-1A-1. A + B is also invertible and (A + B)-1 = A-1 + B-1 A+ B is also invertible and (A + B)-1 = A-i - B-1