2 votes 2 votes If A is a non singular matrix and $\left (I - A + A^{2} - ..... + (-1)^{n}A^{n}\right ) =0$) Then $A^{-1}$ is Linear Algebra engineering-mathematics linear-algebra matrix + – anonymous asked Aug 10, 2017 anonymous 491 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes $\left ( I-A+A^{2}-\cdots+(-1)^{n}A^{n} \right )=0$ $I=\left ( A-A^{2}+A^{3}\cdots +(-1)^{n+1}A^{n+1} \right )$ Multiply both size by $A^{-1}$ $A^{-1}=\left ( I-A+A^{2}\cdots +(-1)^{n+1}A^{n} \right )$ Tesla! answered Aug 10, 2017 edited Oct 5, 2017 by Tesla! Tesla! comment Share Follow See 1 comment See all 1 1 comment reply syed aamiruddin commented Oct 5, 2017 reply Follow Share it should be A−1=(I−A+A2⋯+(−1)n+1 An-1) 0 votes 0 votes Please log in or register to add a comment.