Determinants Te...

If $$x, y, z$$ are positive numbers, then value of the determinant $$\begin{vmatrix}1 & log_xy & log_xz \\ log_yx & 1 & log_yz\\ log_zx & log_zy & 1\end{vmatrix}$$ is equal to

If $$\Delta =\begin{vmatrix} a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3\end{vmatrix}$$ and $$A_2, B_2, C_2$$ are respectively cofactors of $$a_2, b_2, c_2$$ then $$a_1A_2 + b_1B_2 + c_1C_2$$ is equal to

If [a] denotes the greatest integer less than or equal to a and $$-1 \leq x < 0, 0 \leq y < 1, 1 \leq z < 2$$, then $$\begin{vmatrix}[x]+1 & [y] & [z] \\ [x] & [y]+1 & [z] \\ [x] & [y] & [z]+1\end{vmatrix}$$ is equal to

If cofactor of 2x in the determinant $$\begin{vmatrix}x & 1 & -2 \\ 1 & 2x & x-1 \\ x-1 & x & 0\end{vmatrix}$$ is zero, then $$x$$ equals to

If $$A =$$$$\displaystyle \begin{bmatrix}\alpha  & 2\\ 2 & \alpha \end{bmatrix}$$ and $$\displaystyle \left | A \right |^{3}=125$$ then the value of $$\displaystyle \alpha $$ is

If A and B are square matrices of order 3, then 
 

If $$A=\begin{bmatrix} 3 & 2 \\ 1 & 4 \end{bmatrix}$$, then $$A(Adj. A)$$ equals-

If $$A=\begin{bmatrix} 1 & -2 & 3 \\ 4 & 0 & -1 \\ -3 & 1 & 5 \end{bmatrix}$$, then $${(adj. A)}_{23}$$ is equal to