Spectrum of an operator$(Ax)(t) = a(t)x(t)$ in $C[0,1]$

Question

Let $X = C[0,1]$ and define $A:X \to X$ where $(Ax)(t) = a(t)x(t), a\in C[0,1]$

I want to solve problem that similar to this, but I want to understand how to find spectrum of this operator.

I only started learning Spectral Theory, so can anyone help clear up some of the ideas. Any ideas are appreciated.

//I already see other q/a, but it does not help.