# Matrix Algebra

1. Sep 30, 2005

### Ahmes

Hello,
I have to calculate the trace of the following matrix: $$(A+I)^{-1}$$
where $$A$$ is:
$$1 0 0 1$$
$$0 2 2 0$$
$$0 2 2 0$$
$$1 0 0 1$$
and $$I$$ is the unit matrix 4x4.
The calculations are extremely excruciating and the result is $$38/15$$ [checked]. I'm afraid I miss the whole point of this. Can the fact the matrix is diagonalizable help me reach the answer faster?
I mean not going through the process of adding 1 to the diagonal elements and do the inverse.

Thank you.

2. Sep 30, 2005

### Hurkyl

Staff Emeritus
It would if you could get the trace of A from its diagonalization!