Express the following matrices as the sum of a symmetric and a skew symmetric matrix : $\left[\begin{array}{ccc}3 & 3 & -1 \\ -2 & -2 & 1 \\ -4 & -5 & 2\end{array}\right]$

Let $A$ is a symmetric and $ \,B$ is a skew symmetric matrix, such that  $A – B = \left[ {\begin{array}{*{20}{c}}
  1&2 \\ 
  3&4 
\end{array}} \right]$, then $|A|$ is

Let $A$ and $B$ be any two $3\times3$ matrices. If $A$ is symmetric and $B$ is skewsymmetric, then the matrix $AB – BA$ is

An orthogonal matrix is

Let $A =\left[\begin{array}{ll} a & b \\ c & d \end{array}\right]$ and $B =\left[\begin{array}{l}\alpha \\ \beta\end{array}\right] \neq\left[\begin{array}{l}0 \\ 0\end{array}\right]$ such that
$AB = B$ and $a + d =2021,$ then the value of $ad – bc$ is equal to …… .