If the vectors $$\alpha = \widehat i + a\widehat j + {a^2}\widehat k,\,\beta = \widehat i + b\widehat j + {b^2}\widehat k$$ and $$\,\gamma = \widehat i + c\widehat j + {c^2}\widehat k$$ are three non-coplanar

vectors and $$\left| {\matrix{ a & {{a^2}} & {1 + {a^3}} \cr b & {{b^2}} & {1 + {b^3}} \cr c & {{c^2}} & {1 + {c^3}} \cr } } \right| = 0$$, then the value of abc is

Let A be a square matrix of order 3 whose all entries are 1 and let I₃ be the identity matrix of order 3. Then, the matrix $$A - 3{I_3}$$ is

If M is any square matrix of order 3 over R and if M' be the transpose of M, then adj(M') $$-$$ (adj M)' is equal to

If $$A = \left( {\matrix{ 5 & {5x} & x \cr 0 & x & {5x} \cr 0 & 0 & 5 \cr } } \right)$$ and $$|A{|^2} = 25$$, then | x | is equal to