If S is the set of distinct values of 'b' for which the following system of linear equations

x + y + z = 1
x + ay + z = 1
ax + by + z = 0

has no solution, then S is :

If    A = $$\left[ {\matrix{ { - 4} & { - 1} \cr 3 & 1 \cr } } \right]$$,

then the determinant of the matrix (A²⁰¹⁶ − 2A²⁰¹⁵ − A²⁰¹⁴) is :

Let A be a 3 $$ \times $$ 3 matrix such that A² $$-$$ 5A + 7I = 0

Statement - I :  

A^$$-$$1 = $${1 \over 7}$$ (5I $$-$$ A).

Statement - II :

The polynomial A³ $$-$$ 2A² $$-$$ 3A + I can be reduced to 5(A $$-$$ 4I).

Then :

The number of distinct real roots of the equation,

$$\left| {\matrix{ {\cos x} & {\sin x} & {\sin x} \cr {\sin x} & {\cos x} & {\sin x} \cr {\sin x} & {\sin x} & {\cos x} \cr } } \right| = 0$$ in the interval $$\left[ { - {\pi \over 4},{\pi \over 4}} \right]$$ is :