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I have to calculate the trace of the following matrix: [tex](A+I)^{-1}[/tex]

where [tex]A[/tex] is:

[tex]1 0 0 1[/tex]

[tex]0 2 2 0[/tex]

[tex]0 2 2 0[/tex]

[tex]1 0 0 1[/tex]

and [tex]I[/tex] is the unit matrix 4x4.

The calculations areextremely excruciatingand the result is [tex]38/15[/tex] [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.

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# Homework Help: Matrix Algebra

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