(Solved): Linear algebra, matrix: a. Show that for any square matrix \( \mathbf{A} \), the matrix \( \mathbf{ ...

Linear algebra, matrix:

a. Show that for any square matrix \( \mathbf{A} \), the matrix \( \mathbf{A}+\mathbf{A}^{T} \) is symmetric. b. Define a matrix \( \mathbf{A} \) to be skew-symmetric if \( \mathbf{A}^{T}=-\mathbf{A} \). Show that for any the matrix \( \mathbf{A}-\mathbf{A}^{T} \) is skew-symmetric.