I have 5 T-F statements right here about symmetric matrices, and to the right are my attempts. I have a feeling some of them are wrong, though.
(a) Symmetric matrices must be square. (T)
There can be a rectangular matrix which is symmetrical.
(b) A scalar is symmetric. (T)
I don't know why
(c) If $A$ is symmetric, then $ \alpha A$ is symmetric. (T)
What is $\alpha A$?
(d) The sum of symmetric matrices is symmetric.
I think this is false as not all sums will be symmetric.
(e) If $(A')' = A$ , then $A$ is symmetric.
I think this is true.
Could I encourage that, if you know one part of the answer, please go ahead to answer them? I know that it will be very, very hard to find one answer with all 5.