Question

The rank of matrix A of order 2 x 2 is 1 then the determinant of A is​

Answer 1

Answer:

Let the 2×2 matrix be

A=(acbd)

Given a, b, c and d are non-zero and the determinant

∣∣∣acbd∣∣∣=0

Therefore, rank is not equal to 2.

Then go for all possible 1×1 matrices from the given 2×2 matrix.

(a)

(b)

(c)

(d)

We should check whether atleast one of these matrices have non-zero determinant.

Since all these 1×1 matrices are non-zero, their determinants are also non-zero.

Thus, rank = 1