Invertible Matrices

Step 1: Understanding the Concept:
We are dealing with matrix powers and transformations. Note that for matrix , and (the identity matrix), because is an involutory matrix.

Step 2: Key Formula or Approach:
If , then . Since , the inner terms cancel out.

Step 3: Detailed Explanation:
1. We need to find .
2. Substitute : 3. Since , we have 4. For , the power follows the pattern: 5. Therefore,

Step 4: Final Answer
The result is .