Work on the following problems using Mathematica:

1. Example 1.4: Calculate 3A, A+B, B-A, A+C, CB, the transpose of B, the square of C.

2. Example 1.8: Solve the linear systems in (i)-(iv).

3. Example 1.10: Find the inverses of the matrices in (i)-(iii).

4. Example 1.12: Find the determinant of the matrix in (iv).

5. Example 1.14: Find all eigenvalue and eigenvectors of the matrices in (i)-(v).

6. Example 1.17: Find the powers of the matrices in (i)-(iv).