The

**power**, n,

**of a matrix**, A, is when you multiply the matrix by itself n times.

**A matrix can only be raised to a power if it has the same number of rows and columns**. Below you can visualize how to take the power of a matrix. (Note: The matrix is being multiplied by itself n times)

- Rewrite the problem (expand)
- Multiply the first two matrices
- Multiply the next matrix (if there is one) to the matrix produced in step 2
- Multiply the next matrix (if there is one) to the matrix produced in step 3

And so on until you get your final matrix.

Let’s see some examples of how to take the power of a matrix to better understand..

First example (click here):

1. Rewrite the problem

2. Multiply the first two matrices

1. Rewrite the problem

2. Multiply the first two matrices

3. Multiply the next matrix to the matrix produced in step 2

1. Rewrite the problem

2. Multiply the two matrices

Until next time,

Leah

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