Answer
(a) The unit matrix $I_2$, that is
$$I_2=\left[\begin{array}{ll}{1} & {0} \\ {0} & {1}\end{array}\right].$$
(b) The matrices on the form
$$\left[\begin{array}{ll}{1} & {a} \\ {0} & {0}\end{array}\right], \quad a\in R.$$
For example, the matrix $$\left[\begin{array}{ll}{1} & {3} \\ {0} & {0}\end{array}\right].$$
Work Step by Step
The possible $2\times 2$ reduced row-echelon matrices can be one of the following forms:
(a) The unit matrix $I_2$, that is
$$I_2=\left[\begin{array}{ll}{1} & {0} \\ {0} & {1}\end{array}\right].$$
(b) The matrices on the form
$$\left[\begin{array}{ll}{1} & {a} \\ {0} & {0}\end{array}\right], \quad a\in R.$$
For example, the matrix $$\left[\begin{array}{ll}{1} & {3} \\ {0} & {0}\end{array}\right].$$
