The correct option is D 1 if a = -6
A=∣∣
∣∣−1252−4a−41−2a+1∣∣
∣∣=∣∣
∣∣00a+600−a−61−2a+1∣∣
∣∣
(Operating (R1→R1+R3andR2→R2−2R3)
=∣∣
∣∣00000−a−61−2a+1∣∣
∣∣(Operating R1→R1+R2)
When a=−6,A=∣∣
∣∣0000001−2−5∣∣
∣∣, ∴ρ(A)=1
Where ρ(A)number of non-zero rows
When a=6,A=∣∣
∣∣00000−121−27∣∣
∣∣,∴ρ(A)=2
When a=1,A=∣∣
∣∣00000−71−22∣∣
∣∣,∴ρ(A)=2
When a=2,A=∣∣
∣∣00000−81−22∣∣
∣∣,∴ρ(A)=2