The first question:

a. Use matrix multiplication to show that if

**x**is a solution of the homogeneous system

_{0}**Ax**=

**0**and

**x**is a solution of the nonhomogeneous system

_{1}**Ax**=

**b**, then

**x**+

_{0}**x**is also a solution of the nonhomogeneous system.

_{1}b. Suppose that

**x**and

_{1}**x**are solutions of the nonhomogeneous system of part (a). Show that

_{2}**x**-

_{1}**x**is a solution of the homogeneous system

_{2}**Ax**=

**0**.

The second question:

Let

**A**be an

*n*x

*n*matrix such that

**Ax**=

**x**for every

*n*-vector

**x**. Show that

**A**=

**I**.