Determinants Te...

$$\left| \begin{matrix} 1+i & 1-i & i \\ 1+i & i & 1+i \\ i & 1+i & 1-i \end{matrix} \right| $$ (where $$i=\sqrt {-1}$$) equals.

If $$\displaystyle{\left| {_2^{4\,}\,\,_1^1} \right|^2} = \left| {_1^3\,\,_x^2} \right| - \left| {_{ - 2}^x\,\,_1^3} \right|,$$ then $$x$$=

`If $$(8,1),(k,-4),(2,-5)$$ are collinaer, then $$k=$$

If $$A=\left[ \begin{matrix} 0 & 1 \\ -1 & 0 \end{matrix} \right] $$ then determinant of $$[A]$$ is

$$\left| \begin{matrix} 1& a & a^2 \\ 1 & b & b^2 \\ 1 & c & c^2 \end{matrix} \right| =$$

If the points $$(a, 1), (2, -1)$$ and $$\left(\dfrac{1}{2}, 2\right)$$ are collinear, then $$a$$ is equal to:

If $$A=\begin{bmatrix} 5 & 1 \\ 2 & 3 \end{bmatrix}$$, the determinant of matrix $$A$$ is

Find the determinant:
$$\begin{vmatrix} 1 & 2 & 1 \\ 2 & 2 & 2 \\ 3 & 1 & 4 \end{vmatrix}$$

What is the value of the determinant
$$\begin{vmatrix}  1!& 2! &  3!\\ 2! & 3! & 4! \\  3!&  4!&  5!\end{vmatrix}$$$$?$$

lf $$\mathrm{A}=\left[\begin{array}{lll}
1 & 5 & -6\\
-8 & 0 & 4\\
3 & -7 & 2
\end{array}\right]$$, then the cofactor of -7=......