If $A = \left[ {\begin{array}{*{20}{c}}{{{\cos }^2}\theta }&{\sin \theta \cos \theta }\\{\sin \theta \cos \theta }&{{{\sin }^2}\theta }\end{array}} \right]$, $B = \left[ {\begin{array}{*{20}{c}}{{{\cos }^2}\phi }&{\sin \phi \cos \phi }\\{\sin \phi \cos \phi }&{{{\sin }^2}\phi }\end{array}} \right]$ and $\theta $ and $\phi $ differs by $\frac{\pi }{2},$ then $AB = $

If $p, q, r$ are $3$ real numbers satisfying the matrix equation, $[p\,q\,r]\,\left[ {\begin{array}{*{20}{c}}
3&4&1\\
3&2&3\\
2&0&2
\end{array}} \right] = [3\,\,\,0\,\,\,1]$ then $2p + q – r$ equals

If $A = \left[ {\begin{array}{*{20}{c}}1&0&0&0\\2&3&0&0\\4&5&6&0\\7&8&9&{10}\end{array}} \right]$, then $A$ is

Let $M =\left[\begin{array}{cc}0 & -\alpha \\ \alpha & 0\end{array}\right]$, where $\alpha$ is a non-zero real number an $N =\sum\limits_{ k =1}^{49} M ^{2 k }$. If $\left( I – M ^{2}\right) N =-2 I$, then the positive integral value of $\alpha$ is

If $A$ is a $m \times n$matrix and $B$ is a matrix such that both $AB$ and $BA$ are defined, then the order of $B$ is