If the system of linear equations
x + ay + z = 3
x + 2y + 2z = 6
x + 5y + 3z = b
has no solution, then :

Let $$A$$ be a matrix such that $$A.\left[ {\matrix{ 1 & 2 \cr 0 & 3 \cr } } \right]$$ is a scalar matrix and |3A| = 108.
Then A² equals :

Let S be the set of all real values of k for which the systemof linear equations
x + y + z = 2
2x + y $$-$$ z = 3
3x + 2y + kz = 4
has a unique solution. Then S is :

For two 3 × 3 matrices A and B, let A + B = 2B^T and 3A + 2B = I₃, where B^T is the transpose of B and I₃ is 3 × 3 identity matrix. Then :