$5.$The current mirror circuit is given below:

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a$)$ Prove $I_{\text{R}\text{E}\text{F}}=I_{Q1},$ assuming all the process and geometrical parameters of $M_3$ and $M_2$ are same.

b$)$ Why $M_3$ is always in saturation? Explain mathematically.

c$)I_{\text{R}\text{E}\text{F}1}$ and not the gate source voltage, controls and determines the current in the entire current mirror circuit. How?