Question

If a matrix is both symmetric and skew symmetric, then

• A. A is a diagonal matrix
• B. A is a zero matrix
• C. A is a scalar matrix
• D. A is a square matrix

Hint:

If a matrix satisfies both symmetric and skew-symmetric conditions, it must be a zero matrix.

Answer 1

The Correct Option is B

Concept:
• Symmetric matrix: \(A^T = A\)
• Skew-symmetric matrix: \(A^T = -A\)

Step 1: Given both conditions. \[ A^T = A \quad \text{and} \quad A^T = -A \]

Step 2: Equate both. \[ A = -A \]

Step 3: Solve. \[ 2A = 0 \Rightarrow A = 0 \]

Step 4: Conclusion. All elements of matrix are zero. \[ \boxed{\text{Zero matrix}} \]