If the matrix $\begin{bmatrix} a & 2 & -3 \\ b & 0 & 4 \\ c & -4 & 0 \end{bmatrix}$ is a skew-symmetric matrix,then $a+b+c=$

An orthogonal matrix is

If $A$ is a square matrix, then which of the following is true?

If $A = \begin{bmatrix} 1 & -1 & 2 \\ -2 & 3 & -3 \\ 4 & -4 & 5 \end{bmatrix}$ is the given matrix and $A^T$ represents the transpose of $A$,then $AA^T - A - A^T =$

If $A=\begin{bmatrix}-1 & 2 & 3 \\ 5 & 7 & 9 \\ -2 & 1 & 1\end{bmatrix}$ and $B=\begin{bmatrix}-4 & 1 & -5 \\ 1 & 2 & 0 \\ 1 & 3 & 1\end{bmatrix}$,then verify that $(A+B)^{\prime}=A^{\prime}+B^{\prime}$.

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