Diagonal matrix/Eigenspaces/Geometric multiplicity/Exercise

Determine the eigenvalues, the eigenspaces, and the geometric multiplicities of the matrix

${\begin{pmatrix}2&0&\cdots &\cdots &\cdots &0\\0&1&\ddots &\ddots &\vdots &\vdots \\\vdots &\ddots &3&\ddots &\ddots &\vdots \\\vdots &\ddots &\ddots &1&\ddots &\vdots \\\vdots &\vdots &\ddots &\ddots &3&0\\0&\cdots &\cdots &\cdots &0&1\end{pmatrix}}.$

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