If $$\left| {\matrix{ x & y & 0 \cr 0 & x & y \cr y & 0 & x \cr } } \right| = 0$$, then which one of the following is correct?

For a square matrix A, which of the following properties hold?

1. $${({A^{ - 1}})^{ - 1}} = A$$

2. $$\det \,({A^{ - 1}}) = {1 \over {\det \,A}}$$

3. $${(\lambda A)^{ - 1}} = \lambda {A^{ - 1}}$$, where $$\lambda$$ is a scalar

Select the correct answer using the code given below.

Which one of the following factors does the expansion of the determinant

$$\left| {\matrix{ x & y & 3 \cr {{x^2}} & {5{y^3}} & 9 \cr {{x^3}} & {10{y^5}} & {27} \cr } } \right|$$ contain?

If a + b + c = 0, then one of the solutions of $$\left| {\matrix{ {a - x} & c & b \cr c & {b - x} & a \cr b & a & {c - x} \cr } } \right| = 0$$ is