Degree of the characteristic polynomial is same as n

• They don’t prove it but it’s true.
• It makes sense cuz $\lambda I=\left[\begin{array}{cc}\lambda & 0\\ 0& \lambda \end{array}\right]$, so det(A - $\lambda I$) should have some sort of multiplication between those $n$ number of $\lambda$ terms.

Extending this,

• Since $C_A(\lambda )$ has $n$ roots, there can be maximum $n$ distinct eigenvalues.
• This connects to Algebraic Multiplicity of an Eigenvalue.