# Characteristic Roots of Matrix

### Characteristic Roots of Matrix

Can someone solve this, or at least gave me a hint?
a) Prove that a square matrix A has non-zero determinant (i.e. non-singular) if, and only if, the characteristic equation of A has all non-zero roots.
b) Show that if a 4x4 matrix has determinant zero, then one of the root of characteristic equation is zero.
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