plz give a detailed answer. leave the calculation just explain how to solve it. thankx.

Hello student
First of all it is important to be well versed with the concept of rank of a matrix. By definition:
A number ‘r’ is called the rank of an m x n matrix if:
1. Every square sub-matrix of order (r+1) or more is singular and
2. There exists at least one square sub-matrix of order r which is non-singular.
Hence, here since it is given that the rank of the matrix is 1, this means there does not exist any non-singular square sub-matrix of order more than 1. Hence, using this we have that the value of the 2x2 determinant must be zero, i.e.

This gives a = -6.
Hence, the correct option is (c).