Answer
20 forms
Work Step by Step
Given: $(A-5I)^2=0$ for a matrix $11 \times 11$ matrix $A$ has $\lambda =2$ with multiplicity $4$. Then there will be 5 possible Jordan block sizes.
Where $\lambda =5$ with multiplicity $6$, there are 4 possible Jordan block sizes.
$2,2,2\\
2,2,1,1\\
2,1,1,1,1\\
1,1,1,1,1,1$
Hence, the number of Jordan canonical forms is: $5 \times 4=20$
