Matrices

We are given the matrix:

and the equation:

We need to determine:

Step 1: Understanding

Rewriting the given expression:

which simplifies to:

Since the sum of all elements of a matrix trace remains invariant under similar transformations, the trace of will be equal to the trace of , which simplifies to:

Step 2: Compute

By properties of matrix inverses and their summation properties, it turns out that:

Final Answer:

Step 1: We are given that

To find , divide the matrix by 5:

Step 2: Now, multiply by to obtain the identity matrix :

Step 3: Next, compute . The result of this calculation is:

Therefore, the correct answer is .