Explanation:

- Matrix A: Identity matrix of order 3. It is a 3x3 matrix with 1s on the diagonal and 0s elsewhere.

- Matrix B: Transpose of matrix A. Since A is an identity matrix, its transpose is the same as A. Therefore, B is also an identity matrix of order 3.

- Matrix C: Sum of A and B, i.e., C = A + B. Since A and B are both identity matrices, each diagonal element of C becomes 2, while off-diagonal elements stay 0.

- Matrix Representation: C = [[2, 0, 0], [0, 2, 0], [0, 0, 2]] (This is a scalar multiple of the identity matrix).

- Determinant Calculation: The determinant of a diagonal matrix is the product of its diagonal elements. Therefore, determinant of C = 2 * 2 * 2 = 8.

Correct Answer: ?? Option 4: 8