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.