The number of right inverses for the matrix [(1, -1, 2), (2, -1, 1)] is

Question

Let A be an m × n matrix. If there exists a matrix L of type n × m such that LA = I_n, then L is called left inverse of A. Similarly, if there exists a matrix R of type n × m such that AR = I_m, then R is called right inverse of A.

For example, to find right inverse of matrix

⇒ x - u = 1

y - v = 0

z - w = 0

x + u = 0

y + v = 1

z + w = 0

2x + 3u = 0

2y + 3v = 0

2z + 3w = 1

As this system of equations is inconsistent, we say there is no right inverse for matrix A

The number of right inverses for the matrix [(1, -1, 2), (2, -1, 1)] is

(A) 0

(B) 1

(C) 2

(D) Infinite

Answer 1

Answer is (D) Infinite

Let right inverse be

Now,

a - c + 2e = 1

b - d + 2f = 0

2a - c + e = 0

2b - d + f = 1

Therefore, infinite solutions