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

What is the value of the determinant

$$\left| {\matrix{ 1 & 1 & 1 \cr 1 & {1 + xyz} & 1 \cr 1 & 1 & {1 + xyz} \cr } } \right|$$ ?

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.