Determine whether the statement is true or false. if it is true, explain why. if it is false, explain why or give an example that disaproves the statement.
if ax=ax for a square matrix a, vector x, and scalar a, where x=/0, then a is an eigenvalue of a.

True

Step-by-step explanation:

This statement is true, basically by the definition of eigenvalue. An eigenvalue is a scalar λ such that there exist a nonzero vector v which satisfies Av = λv. Naturally, the given value a satisfies this hypothesis, hence it is an eigenvalue, as we wanted to show.