Inverse of I-A

[star321]

hi,, what is the inverse of (I-A)? Where I is identity matrix and A is nonsigular matrix

 

[daon2]

Why do you assume there is one? For example take A=I.

 

[star321]

Why do you assume there is one? For example take A=I.

i asked abt (I-A)^-1?not just I-A so i cant take I=A

 

[daon2]

i asked abt (I-A)^-1?not just I-A so i cant take I=A

You did not comprehend my post. What you are asking is impossible.

 

[Bob Brown MSEE]

\(\displaystyle A^{-1}\, \cdot\, \left(A^{-1}\, -\, I\right)^{-1}\)

 

[HallsofIvy]

i asked abt (I-A)^-1?not just I-A so i cant take I=A

You can't because then it doesn't have an inverse. That was daon2's point. The fact that A is invertible does NOT imply that I- A is invertible. Here's another example:
\(\displaystyle A= \begin{pmatrix}1 & 0 \\ 1 & 2 \end{pmatrix}\) which has an inverse.
then \(\displaystyle I- A= \begin{pmatrix}0 & 0 \\ -1 & -1 \end{pmatrix}\) which has no inverse.