Here's how to solve the problem:**1. Find the square of matrix A:***
**2. Define the identity matrix:*** The identity matrix of order 2x2 is:
**3. Substitute into the equation:*** The equation is:
* Substitute the matrices:
**4. Simplify the equation:*** This gives us:
**5. Solve for m and n:*** By comparing corresponding elements, we get the following system of equations: * m + n = 9 * 4m = 16 * 2m = 8 * 3m + n = 17* Solving for m, we find m = 4.* Substituting m = 4 into the first equation, we find n = 5.**6. Calculate m - n:*** m - n = 4 - 5 = -1**Therefore, the answer is B. -1**