The question is :
Let $A$ be an $n \times n$ diagonalisable matrix whose eigen values are $1,3,6$ with some unknown multiplicity.Is the matrix $2A^2-A+23I$ diagonalisable?
I dont find any proper way to proceed.Please help me.
Thank you in advance.
EDIT :
I think if $A$ is similar to a diagonal matrix $D$ then $2A^2-A+23I$ is similar to a diagonal matrix $2D^2-D+23I$.Isn't it?Hence $2A^2-A+23I$ becomes diagonalisable.