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## Homework Statement

For each of the following, give an example if it exists. If it doesn't exist, explain why.

a) An invertible 3x3 matrix which is not diagonalizable.

c) An 3x3 matrix A with A^6+I3=0 (Hint: Use the determinant)

## Homework Equations

For a):

I know in order for a matrix to be diagonalizable, the matrix A has to be similar with D (Diagonal Matrix). Which means having the same eigenvalues... Since the eigenvalues are on the main diagonal. All invertible matrix cant have 0 in the main diagonal in the reduced echelon form so it has to be diagonalizable so it does not exist...I am pretty sure this is not a good explanation, so I am asking for some clarification on diagonalization properties for invertible matrixe.

for b): I used the determinant like this: DetA^6 = -detI3 => (DetA)^6= -1. So it does not exist...Is it what the question meant?

I am not good with algebra so forgive me for my misunderstandings.