If $$A = \left[ {\matrix{ \alpha & 2 \cr 2 & \alpha \cr } } \right]$$ and det (A³) = 125, then $$\alpha$$ is equal to

If B is a non-singular matrix and A is a square matrix, then the value of det (B^$$-$$1 AB) is equal to

If a $$\ne$$ b $$\ne$$ c, then one value of x which satisfies the equation $$\left| {\matrix{ 0 & {x - a} & {x - b} \cr {x + a} & 0 & {x - c} \cr {x + b} & {x + c} & 0 \cr } } \right| = 0$$ is given by

The equations $$x + 2y + 3z = 1$$, $$2x + y + 3z = 2$$, $$5x + 5y + 9z = 4$$