Conjugate of a Matrix

Q. $\left(\begin{array}{cc}2i& 9+2i\\ -9+2i& 3i\end{array}\right]\mathrm{is}a\mathrm{skew}\mathrm{hermitian}\mathrm{matrix}.$

1. False
2. True

Q.

Imaginary part of third element of the second row for the Conjugate of $\left[\begin{array}{ccc}3+4i& 4& 2+5i\\ 1+2i& 2+3i& 3+5i\\ 2+7i& 9& 5\end{array}\right]$ is

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Q. All the elements in a matrix A are complex numbers with imaginary parts not equal to zero. If $A^{\ast }$ is the conjugate of the matrix A, $a_{ij}$ is the general element of matrix A, then what is the general element of the matrix, $\frac{A+A^{\ast }}{2}.$

1. $2lm\left(a_{ij}\right)$
2. $lm\left(a_{ij}\right)$
3. $Re\left(a_{ij}\right)$
4. $\frac{Re\left(a_{ij}\right)}{2}$

Q.

If (i, j)th element of matrix A is 2+3i , what is the corresponding element in A* or conjugate of A.

1. -2 - 3i

2. 3 + 2i

3. 2 - 3i

4. 3 - 2i