Let $$A = \left[\begin{array}{ccc} -3 &1 &-3\cr 3 &5 &-3\cr 2 &-1 &1 \end{array}\right].$$ Compute the following.

$A + A^T =$ $\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$

$A - A^T =$ $\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$

For any square matrix $A$, is the matrix $A+A^T$ lower triangular, upper triangular, symmetric, skew-symmetric, or none of these?
Choose Lower triangular Upper triangular Symmetric Skew-symmetric None of these

For any square matrix $A$, is the matrix $A-A^T$ lower triangular, upper triangular, symmetric, skew-symmetric, or none of these?
Choose Lower triangular Upper triangular Symmetric Skew-symmetric None of these