Question

If the matrix \(A\) is both symmetric and skew symmetric,then

• A. \(A\) is a diagonal matrix
• B. \(A\) is a zero matrix
• C. \(A\) is a square matrix
• D. None of these

Answer 1

The Correct Option is B

The correct answer is B:\(A\) is a zero matrix
\(A'=A\,\, and\,\, A'=-A\)
\(\implies A=-A\)
\(\implies A+A=0\)
\(\implies 2A=0\)
\(\implies A=0\)
Therefore, \(A\) is a zero matrix.