Question

Prove that if b is a square matrix then b+b^t is symmetric

Answer 1

A matrix
`\mathbf X` is symmetric if
`\mathbf X=\mathbf X^\top`. We have


`(\mathbf B+\mathbf B^\top)^\top=\mathbf B^\top+(\mathbf B^\top)^\top=\mathbf B^\top+\mathbf B=\mathbf B+\mathbf B^\top`

and so
`\mathbf B+\mathbf B^\top` is indeed symmetric.