Transpose of a matrix

Q.

If $A$ is a square matrix, then

1. $A+A^T$ is symmetric

2. $A{A}^T$ is skew-symmetric

3. $A^T+A$ is skew-symmetric

4. $A^T$ is skew-symmetric

Q. If A', B' are transpose matrices of the square matrices A, B respectively , then (AB)' is equal to

1. A'B'
2. B'A'
3. AB'
4. BA'

Q. Which among the following would be obtained on simplifying the expression $(A^{T}BA{)}^T$.

1. $A^T{B}^T{A}^T$
2. $A^T{B}^{T}A$
3. $A{A}^T{B}^T$
4. $B^T{A}^{T}A$

Q.

If A and B are two square matrices which are skew symmetric then$(AB{)}^T$ equals to

1. BA
2. -AB
3. -BA
4. AB

Q.

If $A=\left[\begin{array}{cc}1& tanx\\ -tanx& 1\end{array}\right],A^T{A}^{-1}=$ ___

1. $\left[\begin{array}{cc}cos2x& -sin2x\\ sin2x& cos2x\end{array}\right]$

2. $\left[\begin{array}{cc}cos2x& sin2x\\ -sin2x& cos2x\end{array}\right]$

3. $\left[\begin{array}{cc}1-ta{n}^{2}x& 2tanx\\ -2tanx& 1-ta{n}^{2}x\end{array}\right]$

4. $\left[\begin{array}{cc}1-ta{n}^{2}x& -2tanx\\ 2tanx& 1-ta{n}^{2}x\end{array}\right]$