The matrix $A = \left[ {\begin{array}{*{20}{c}}{1/\sqrt 2 }&{1/\sqrt 2 }\\{ – 1/\sqrt 2 }&{ – 1/\sqrt 2 }\end{array}} \right]$ is

If  $A=\left[\begin{array}{cc}\cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha\end{array}\right],$ then verify that $A^{\prime} A=I$

Given $A$ and $C$ are involutary matrices and $B$ is a non-singular matrix, then $(AB^{-1}C)^{-1}$ is equal to –

Let $A =\left[\begin{array}{ll} a & b \\ c & d \end{array}\right]$ and $B =\left[\begin{array}{l}\alpha \\ \beta\end{array}\right] \neq\left[\begin{array}{l}0 \\ 0\end{array}\right]$ such that
$AB = B$ and $a + d =2021,$ then the value of $ad – bc$ is equal to …… .

If $ A$  is a square matrix, then which of the following matrices is not symmetric