Skew Hermitian Matrix

Q.

Which of the following represents the condition for a matrix A to be skew hermitian Matrix. Given that the general element of the matrix is aij.

1. $aij=-\overline{aij}$

2. $aij=\overline{aji}$

3. $aij=-\overline{aji}$

4. $\overline{aij}=-aij$

Q.

If A is a square matrix then $A-\overline{A^T}$ is a skew hermitian matrix.

1. True

2. False

Q.

In a square matrix of order 4, the element $a_{33}$ = 33. This square matrix cannot be skew hermitian.

1. True

2. False

Q.

Which among the following is/are skew hermitian matrix.

1. $\left[\begin{array}{cc}o& i\\ i& 0\end{array}\right]$

2. $\left[\begin{array}{ccc}i& 3+i& 5-i\\ -3+i& -i& 0\\ -5-i& 0& 3i\end{array}\right]$

3. $\left[\begin{array}{cc}i+1& 3i\\ 3i& i+1\end{array}\right]$

4. $\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$