For which real values of t does the following system of linear equations:

$$\{\begin{array}{c}t{x}_{1}+{x}_{2}+{x}_{3}=1\\ {x}_{1}+t{x}_{2}+{x}_{3}=1\\ {x}_{1}+{x}_{2}+t{x}_{3}=1\end{array}$$

Have:

a) a unique solution?

b) infinitely many solutions?

c) no solutions?

$$\{\begin{array}{c}t{x}_{1}+{x}_{2}+{x}_{3}=1\\ {x}_{1}+t{x}_{2}+{x}_{3}=1\\ {x}_{1}+{x}_{2}+t{x}_{3}=1\end{array}$$

Have:

a) a unique solution?

b) infinitely many solutions?

c) no solutions?