Question

If a matrix $ A $ is symmetric as well as skew symmetric then $ A $ is

• A. Diagonal matrix
• B. Null matrix
• C. Unit matrix
• D. None of these

Hint:

A matrix that is both symmetric and skew-symmetric must be the null matrix.

Answer 1

The Correct Option is B

Step 1: Symmetric and Skew-Symmetric Matrix Properties
A matrix \( A \) is symmetric if \( A^T = A \).

A matrix \( A \) is skew-symmetric if \( A^T = -A \).

Step 2: Analyzing the Possibilities
For a matrix to be both symmetric and skew-symmetric, we must have \( A^T = A \) and \( A^T = -A \), which implies \( A = -A \).
Therefore, \( A \) must be the zero matrix, which is a null matrix.
Step 3: Conclusion
Thus, \( A \) is a null matrix.