Let A = [a_ij] be a real matrix of order 3 $$\times$$ 3, such that a_i1 + a_i2 + a_i3 = 1, for i = 1, 2, 3. Then, the sum of all the entries of the matrix A³ is equal to :

The value of k $$\in$$R, for which the following system of linear equations

3x $$-$$ y + 4z = 3,

x + 2y $$-$$ 3z = $$-$$2

6x + 5y + kz = $$-$$3,

has infinitely many solutions, is :

Let $$A = \left[ {\matrix{ 2 & 3 \cr a & 0 \cr } } \right]$$, a$$\in$$R be written as P + Q where P is a symmetric matrix and Q is skew symmetric matrix. If det(Q) = 9, then the modulus of the sum of all possible values of determinant of P is equal to :

Let the system of linear equations

4x + $$\lambda$$y + 2z = 0

2x $$-$$ y + z = 0

$$\mu$$x + 2y + 3z = 0, $$\lambda$$, $$\mu$$$$\in$$R.

has a non-trivial solution. Then which of the following is true?