The sum of three numbers is 6 . Twice the third number, when added to the first number gives 7 , On adding the sum of the second and third numbers to thrice the first number, we get 12 . The above situation can be represented in matrix form as $A X=B$. Then the $|\operatorname{adj} A|$ is equal to

If $A(t)=\left[\begin{array}{cc}\cos t & \sin t \\ -\sin t & \cos t\end{array}\right]$ then the product of $A(t)$ and $A(-t)$ is

If $A=\left[\begin{array}{cc}1 & -2 \\ 4 & 5\end{array}\right] ; f(t)=t^2-3 t+7$ then $f(A)+\left[\begin{array}{cc}3 & 6 \\ -12 & -9\end{array}\right]=$

For two matrices $A$ and $B$, given that $A^{-1}=\frac{1}{8} B$ then inverse of $(8 A)$ is