If $A$ is a symmetric $n × n$ matrix and $B$ is a skew symmetric $n × n$ matrix, which of the following are true?
(a) $ABA$ is symmetric
(b) $ABA$ is skew-symmetric
(c) $AB^2A$ is symmetric
(d) $AB^2A$ is skew-symmetric
I know that b and d holds true.
I am unsure of A and C
However, for a, how does multiplying ABA preserve symmetry, but squaring B preserves symmetry as well?