Question

$IfA=\left[\begin{array}{ccc}a& h& g\\ h& b& f\\ g& f& c\end{array}\right]$, then A is

• A. a nilpotent matrix
• B. an involutory matrix
• C. a symmetric matrix
• D. an idempotent matrix

Answer 1

The correct option is C a symmetric matrix

Here The transpose of the matrix A is

$=\left[\begin{array}{ccc}a& h& g\\ h& b& f\\ g& f& c\end{array}\right]$

$\therefore A=A^T$

And a symmetric matrix is a square matrix that is equal to its transpose.

Hence the answer is option C