1. The problem asks us to verify the truth of two matrix equalities for square matrices $M$ and $N$ of the same size. 2. For part (a), the expression is $M^2 - N^2 = (M + N)(M - N)$. 3. Recall that matrix multiplication is generally not commutative, meaning $AB \neq BA$ in general. 4. Expanding the right side: $(M + N)(M - N) = M^2 - MN + NM - N^2$. 5. Since $MN$ and $NM$ may not be equal, $M^2 - N^2 \neq (M + N)(M - N)$ in general. 6. Therefore, part (a) is false. 7. For part (b), the expression is $M^T + N^T = (M + N)^T$. 8. The transpose of a sum of matrices equals the sum of their transposes: $(M + N)^T = M^T + N^T$. 9. This is a standard property of matrix transposition. 10. Therefore, part (b) is true. 11. Since part (b) is true, part (c) "None of the above is true" is false. Final answer: (b) $M^T + N^T = (M + N)^T$ is true.