Question

If A is a skew-symmetric matrix, then trace of A is

• A. 1
• B. -1
• C. 0
• D. None of these

Hint:

If A is a skew-symmetric matrix, then trace of A is

Answer 1

The Correct Option is C

Step 1: Concept
By definition, for a skew-symmetric matrix $A$, $a_{ij} = -a_{ji}$.
Step 2: Analysis
For the diagonal elements where $i = j$, we have $a_{ii} = -a_{ii}$, which implies $2a_{ii} = 0$, so $a_{ii} = 0$.
Step 3: Evaluation
The diagonal elements of any skew-symmetric matrix are always zero.
Step 4: Conclusion
The trace of a matrix is the sum of its diagonal elements. Therefore, Trace of $A = 0 + 0 + ... = 0$.
Final Answer: (c)