We have a set of 3 linear equations in 3 unknowns. 'X \[ \equiv \] Y' means X and Y are equivalent statements and 'X \[\not \equiv \] Y' means X and Y are not equivalent statements.
P : There is a unique solution.
Q : The equations are linearly independent.
R : All eigen values of the coefficient matrix are nonzero.
S : The determinant of the coefficient matrix is nonzero.
Which one of the following is TRUE?

A. \[{\text{P}} \equiv {\text{Q}} \equiv {\text{R}} \equiv {\text{S}}\]

B. \[{\text{P}} \equiv {\text{R}}\not \equiv {\text{Q}} \equiv {\text{S}}\]

C. \[{\text{P}} \equiv {\text{Q}}\not \equiv {\text{R}} \equiv {\text{S}}\]

D. \[{\text{P}}\not \equiv {\text{Q}}\not \equiv {\text{R}}\not \equiv {\text{S}}\]

Answer: Option A