List of top Mathematics Questions on Transpose of a Matrix

Find:
Let \(A=[a_{ij}]\) be a \(2\times2\) matrix whose elements are given by \[ a_{ij}=\frac{(2i-j)^2}{3} \] Find the transpose matrix \(A'\).

If $A = \begin{bmatrix} \cos x & \sin x \\ -\sin x & \cos x \end{bmatrix}$ and $A + A' = I$, then the value of $x \in \left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ is: