**Some Properties of Matrix
Powers**

**Some properties of multiplication of a
matrix by itself to form powers:**

Suppose are matrices and are positive integers.

- Matrix power:

- Zero power:
- Addition of powers:
- Multiplication of powers:
- Distribution of powers: If , then .

**It does not matter in which order you
multiply a matrix by itself to calculate one of its powers.**

**See the spreadsheet screen shot, below,
showing various ways of calculating the fourth power of a matrix A. **

**Note that the third line shows that all
methods of calculating the power yield the same result:**

**Download Microsoft Excel 2002
(2000-compatible) spreadsheet with the above examples:
click here.**

Copyright © 2002-2003 Crystal Sloan