Let $A$ be a skew-symmetric matrix of odd order,then $|A|$ is equal to

$P$ is a $3 \times 3$ square matrix and $\operatorname{Tr}(P) \neq 0$. If $\operatorname{Tr}(P-P^{T})+\operatorname{Tr}(P+P^{T})+\frac{\operatorname{Tr}(P)}{\operatorname{Tr}(P^T)}+\operatorname{Tr}(P) \times \operatorname{Tr}(P^{T})=0$, then $\operatorname{Tr}(P)=$

If $A$ is a square matrix,then $A + A^T$ is:

Which one of the following statements is correct regarding skew-symmetric matrices?

$A, B, C, D$ are square matrices such that $A+B$ is symmetric, $A-B$ is skew-symmetric and $D$ is the transpose of $C$. If $A=\left[\begin{array}{ccc}-1 & 2 & 3 \\ 4 & 3 & -2 \\ 3 & -4 & 5\end{array}\right]$ and $C=\left[\begin{array}{ccc}0 & 1 & -2 \\ 2 & -1 & 0 \\ 0 & 2 & 1\end{array}\right]$, then the matrix $B+D=$

An orthogonal matrix is