Determinants Te...

If $$A+B+C= \pi$$, then $$ \displaystyle \left| \begin{matrix} \tan { \left( A+B+C \right)  }  & \tan { B }  & \tan { C }  \\ \tan { (A+C) }  & 0 & \tan { A }  \\ \tan { (A+B) }  & -\tan { A }  & 0 \end{matrix} \right| $$ is equal to

$$I\mathrm{f}\mathrm{A}=\left[\begin{array}{ll}
1 & 3\\
2 & 1
\end{array}\right]$$, then the determinant $$\mathrm{A}^{2}-2\mathrm{A}$$:

$$\left[\begin{array}{llll}
\mathrm{c}\mathrm{o}\mathrm{s}\alpha+\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{n}\alpha & \mathrm{c}\mathrm{o}\mathrm{s}\beta+\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{n}\beta\\
\mathrm{s}\mathrm{i}\mathrm{n}\beta+\mathrm{i}\mathrm{c}\mathrm{o}\mathrm{s}\beta\ & \mathrm{s}\mathrm{i}\mathrm{n}\alpha+\mathrm{i}\mathrm{c}\mathrm{o}\mathrm{s}\alpha &
\end{array}\right]$$ is

Adj $$\left ( Adj\begin{bmatrix}
2 &-3 \\
4& 6
\end{bmatrix} \right )=$$ 

lf $$\left|\begin{array}{lll}
a+x & a-x & a-x\\
a-x & a+x & a-x\\
a-x & a-x & a+x
\end{array}\right|=0$$ then the non-zero value of x=............ 

A= $$\begin{bmatrix}
3 & 0 & 0\\
0& 3 & 0\\
0& 0 & 3
\end{bmatrix}$$ ,then Adj ( A)

lf $$\left|\begin{array}{lll}
1 & 2 & x\\
4 & -1 & 7\\
2 & 4 & -6
\end{array}\right|$$ is a singular matrix, then $$x$$ is equal to 

If $$\mathrm{A}$$ is an unitary matrix then $$|A|$$ is equal to:

A determinant of second order is made with the elements $$0$$ and $$1.$$ The number of determinants with non-negative values is:

If $$A=\displaystyle \int_{1}^{sin\theta}\frac{t}{1+t^{2}}dt$$ and
$$B=\displaystyle \int_{1}^{cosec\theta}\frac{1}{t(1+t^{2})}dt$$, then the value of determinant  $$\begin{vmatrix}
A & A^{2}& B\\
e^{A+B}& B^{2} &-1 \\
1& A^{2}+B^{2} & -1
\end{vmatrix}$$ is