Let $$a, b$$ and $$c$$ be such that $$b+c \neq 0$$ and $$\begin{aligned} & \left|\begin{array}{ccc} a & a+1 & a-1 \\ -b & b+1 & b-1 \\ c & c-1 & c+1 \end{array}\right| \\ & +\left|\begin{array}{ccc} a+1 & b+1 & c-1 \\ a-1 & b-1 & c+1 \\ (-1)^{n+2} a & (-1)^{n-1} b & (-1)^n c \end{array}\right|=0 \text {, } \\ & \end{aligned}$$

then the value of $$n$$ is

The equation whose roots are the values of the equation $$\left| {\matrix{ 1 & { - 3} & 1 \cr 1 & 6 & 4 \cr 1 & {3x} & {{x^2}} \cr } } \right| = 0$$ is

Let a and b be non-zero real numbers such that $$ab=5/2$$ and given $$A = \left[ {\matrix{ a & { - b} \cr b & a \cr } } \right]$$ and $$A{A^T} = 20I$$ ($$l$$ is unit matrix), then the equation whose roots are a and b is

If $$A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1\end{array}\right], 10 B=\left[\begin{array}{ccc}4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3\end{array}\right]$$ and $$B=A^{-1}$$, then the value of $$\alpha$$ is