Show that for any square matrix, the matrix A +(A)^t is sym

[MidgetDwarf]

Show that for any square matrix, the matrix A + ( A )^t is symmetric.

My attempt. I know that A square matrix has the property that asub (ij). Where i=1,..., m and j=1,..,n.
M=n(same number of rows and columns).

I know that a transpose of a matrix means to interchange the rows with columns.

What I do not understand what it means for a matrix to be symmetric?

 

[MidgetDwarf]

Sorry I forgot the t means the transpose if anyone is confused about my notation.

 

[Nathanael]

What I do not understand what it means for a matrix to be symmetric?

A matrix B is symmetric if B^T=B

In other words B_mn=B_nm for all entries (which also means it must be square). The diagonal entries can be anything because, for example, B₁₁=B₁₁ is always true. But B₁₂ must equal B₂₁, and so on.

(It's easy to understand visually.)