Let $ S = \{A \in a^{n \times n}\mid x^T Ax = 0 , \forall x\in \mathbb{R^n}, A = A^T\} $.
Then
a. $|S|=1$
b. $|S|>1$
c. $|S|=\chi 0$
d. $|S|=0$
My attempt: I know that $x^T Ax = 0$ implies matrix A is skew symmetric. Also, in the question it is given that A is a symmetric matrix. Hence I got zero matrix and so option d, but the actual answer is option a. Please may I know where did I go wrong and how to proceed.