Let $A$ and $B$ be real symmetric matrices of size $n \times n$. Then which one of the following is true?
Option $A$ and $B$ are incorrect because It is not given in question that matrix $A$ is invertible, it may be the case that $A$ is singular matrix.
Option $C$ is incorrect because Matrix multiplicaton are non commutative
A symmetric matrix is a square matrix that is equal to its transpose.
(AB)' = B'A' =BA as Both $A$ and $B$ are symmetric matrices, hence $B' = B$ and $A'=A$
So, (D) is correct option!
Why is $(C)$ not correct option? see the following example:
There are two symmetric matrices given of size $2$x$2$ and $AB != BA$. Therefore (C) is not a correct option!