The number of real values of $t$ such that the system of homogeneous equations:\[tx+(t+1)y+(t-1)z=0\]\[(t+1)x+ty+(t+2)z=0\] \[(t-1)x+(t+2)y+tz=0\] has non-trivial solutions, is

Question

\[(a)\;3 \quad (b)\;2 \quad (c)\;1 \quad (d)\;4 \]