An identity matrix is a square matrix with 1s along its main diagonal (from the top-left to the bottom-right) and 0s elsewhere.

Let's examine the matrices:

• Matrix A: 1 & 0 \\ 0 & 1 \end{bmatrix}$$ This is a 2x2 identity matrix.
• Matrix B: 0 & 1 \\ 1 & 0 \end{bmatrix}$$ This is not an identity matrix because the diagonal does not have all 1s.
• Matrix C: 1 & 1 \\ 1 & 1 \end{bmatrix}$$ This is not an identity matrix because the off-diagonal elements are not 0.
• Matrix D: 0 & 0 \\ 0 & 0 \end{bmatrix}$$ This is not an identity matrix because all elements are 0.

Conclusion:

The identity matrix is Matrix A.

Would you like further details or have any questions?
Here are five related questions to consider:

1. What is the definition of an identity matrix for larger dimensions, like 3x3 or 4x4?
2. How do identity matrices behave under matrix multiplication?
3. Why is the identity matrix important in solving systems of equations?
4. Can non-square matrices ever be identity matrices?
5. What role does the identity matrix play in matrix inverses?

Tip: When multiplying any matrix by an identity matrix, the result will always be the original matrix.