Let $A=\left[\begin{array}{ccccc} -6 &1 &0 &0 &0\cr 0 &-6 &0 &0 &0\cr 0 &0 &-6 &0 &0\cr 0 &0 &0 &1 &0\cr 0 &0 &0 &0 &1 \end{array}\right]$.
Find the geometric multiplicity $d_{-6}$ of the eigenspace $E_{-6}$ of $A$.
$d_{-6} =$
Find the geometric multiplicity $d_{1}$ of the eigenspace $E_{1}$ of $A$.
$d_{1} =$