Algebra of Matrices

If $E\left(\theta \right)=\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right],$ then the value of $E\left(\alpha \right)·E\left(\beta \right)$ is

If $A=\left[\begin{array}{cc}2& -1\\ -1& 2\end{array}\right]$ and $A^2-4A-nI=0,$ then $n$ is equal to

If $A=\left[\begin{array}{cc}{\cos }^2\theta & \cos \theta \sin \theta \\ \cos \theta \sin \theta & {\sin }^2\theta \end{array}\right]$ and $B=\left[\begin{array}{cc}{\cos }^2\varphi & \cos \varphi \sin \varphi \\ \cos \varphi \sin \varphi & {\sin }^2\varphi \end{array}\right],$ and $AB=0,$ then $\theta -\varphi$ is equal

If $A=\left[\begin{array}{lll}1& 2& 2\\ 2& 1& 2\\ 2& 2& 1\end{array}\right]$, then $A^2-4A=$

If $\left[\begin{array}{cc}1& 0\\ 3& -4\end{array}\right]+\left[\begin{array}{cc}a& 1\\ -1& b\end{array}\right]=\left[\begin{array}{cc}2& 1\\ 2& -2\end{array}\right],$ then value of $a, b$ are

If $A=\left[\begin{array}{cc}p& q\\ -q& p\end{array}\right], B=\left[\begin{array}{cc}r& s\\ -s& r\end{array}\right]$, then

If $A=\left[\begin{array}{cc}-1& 2\\ 3& -4\end{array}\right]$, then element $a_{21}$ of $A^2$ is

If $X=\left[\begin{array}{ll}1& a\\ 0& 1\end{array}\right]$ and $3X-\left[\begin{array}{ll}2& 3\\ 0& 2\end{array}\right]=\left[\begin{array}{ll}1& 3\\ 0& 1\end{array}\right]$, then $a$ is equal to

If $\left[\begin{array}{ll}1& 2\\ 2& 1\end{array}\right]\left[\begin{array}{l}\mathrm{x}\\ y\end{array}\right]=\left[\begin{array}{l}5\\ 4\end{array}\right]$, then

If $\left[\begin{array}{ccc}1& x& 2\end{array}\right]\left[\begin{array}{lll}2& 3& 1\\ 0& 4& 2\\ 0& 3& 2\end{array}\right]\left[\begin{array}{l}x\\ 1\\ -1\end{array}\right]=0$, then value of $x$ is

If $I=\left[\begin{array}{ll}1& 0\\ 0& 1\end{array}\right],$ $J=\left[\begin{array}{ll}0& 1\\ -1& 0\end{array}\right]$ and $B=\left[\begin{array}{ll}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right],$ then $B$ is equal to

Which one of the following is not true -

If $A$ and $B$ are two matrices and $\left(A+B\right)\left(A-B\right)=A^2-B^2$, then