Eigenvalues of an nxn matrix

septten

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While looking at past exam papers for an upcoming exam I saw a question: "State if 'A matrix A ∈ Mn×n(R) has at most n different eigenvalues' is true or give a counter example."
At first I thought well yeah thats true because theres only two diagonal entries. Then I remembered examples when I used the quadratic formula and got a minus and plus answers so it must be false?
In an exam I dont have time to do out a huge matrix in REF, does anyone know of a short example to disprove the statement?
 
While looking at past exam papers for an upcoming exam I saw a question: "State if 'A matrix A ∈ Mn×n(R) has at most n different eigenvalues' is true or give a counter example."
At first I thought well yeah thats true because theres only two diagonal entries. Then I remembered examples when I used the quadratic formula and got a minus and plus answers so it must be false?
In an exam I dont have time to do out a huge matrix in REF, does anyone know of a short example to disprove the statement?

An nxn matrix has AT MOST n eigenvalues.
What is the degree of the Characteristic Equation?
What does algebra tell us about the zeros of a n-degree polynomial?
 
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