If $X=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$ and $Y=\left[\begin{array}{cc}0 & 1 \\ -1 & 0\end{array}\right]$ and $B=\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right]$ then $B$ equals :

If $A=\left[\begin{array}{ll}a & b \\ b & a\end{array}\right]$ and $(A I)^2=\left[\begin{array}{ll}\alpha & \beta \\ \beta & \alpha\end{array}\right]$ where I is the identity matrix then

Value of the determinant of a matrix $A$ of order $3 \times 3$ is 7 . Then the value of the determinant formed by the cofactors of matrix A is

If $A=\left[\begin{array}{ccc}4 & \lambda & -3 \\ 0 & 2 & 5 \\ 1 & 1 & 3\end{array}\right]$ then $A^{-1}$ exists if :