Let $$A = \left( {\matrix{ a & b \cr c & d \cr } } \right)$$ be a 2 $$ \times $$ 2 real matrix with det A = 1. If the equation det (A $$ - $$ $$\lambda $$I₂) = 0 has imaginary roots (I₂ be the identity matrix of order 2), then

If $$\left| {\matrix{ {{a^2}} & {bc} & {{c^2} + ac} \cr {{a^2} + ab} & {{b^2}} & {ca} \cr {ab} & {{b^2} + bc} & {{c^2}} \cr } } \right| = k{a^2}{b^2}{c^2}$$,

then K =

If f : S $$ \to $$ R, where S is the set of all non-singular matrices of order 2 over R and $$f\left[ {\left( {\matrix{ a & b \cr c & d \cr } } \right)} \right] = ad - bc$$, then

Let the relation p be defined on R by a p b holds if and only if a $$ - $$ b is zero or irrational, then