Let a, b, c $$ \in $$ R be all non-zero and satisfy
a³ + b³ + c³ = 2. If the matrix

A = $$\left( {\matrix{ a & b & c \cr b & c & a \cr c & a & b \cr } } \right)$$

satisfies A^TA = I, then a value of abc can be :

Let A = {X = (x, y, z)^T: PX = 0 and

x² + y² + z² = 1} where

$$P = \left[ {\matrix{ 1 & 2 & 1 \cr { - 2} & 3 & { - 4} \cr 1 & 9 & { - 1} \cr } } \right]$$,

then the set A :

Let S be the set of all $$\lambda $$ $$ \in $$ R for which the system of linear equations

2x – y + 2z = 2
x – 2y + $$\lambda $$z = –4
x + $$\lambda $$y + z = 4

has no solution. Then the set S :

Let A be a 2 $$ \times $$ 2 real matrix with entries from {0, 1} and |A| $$ \ne $$ 0. Consider the following two statements :

(P) If A $$ \ne $$ I₂ , then |A| = –1
(Q) If |A| = 1, then tr(A) = 2,

where I₂ denotes 2 $$ \times $$ 2 identity matrix and tr(A) denotes the sum of the diagonal entries of A. Then :