Matrix $A$ is defined over real number.
Characteristic polynomial : $p(x)=(x+3)^2(x-1)(x-5)$
It also known that :
- prove $A$ diagonalize.
$-3,1,5$ are eigenvalues, using the characteristic polynomial we can conclude that matrix $A$ is $4 \times 4$
Since eigenvalue $1,5$ has algebraic multiplicity of $1$, we can conclude that geometric multiplicity is also $1$ hence:
I don't find a way to continue from here.