The number of right inverse of the matrix is `[(1,-1, 2),( 2,-1, 1)]`

Let A be an mxxn matrix. If there exists a matrix L of type nxxm such that LA=I_(n) , then L is called left inverse of A. Similarly, if there exists a matrix R of type nxxm such that AR=I_(m) , then R is called right inverse of A. For example, to find right inverse of matrix A=[(1,-1),(1,1),(2,3)] , we take R=[(x,y,x),(u,v,w)] and solve AR=I_(3) , i.e., [(1,-1),(1,1),(2,3)][(x,y,z),(u,v,w)]=[(1,0,0),(0,1,0),(0,0,1)] {:(implies,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

Find the inverse of the matrix A= [(3,1),(4,2)]

The element in the first row and third column of the inverse of the matrix [(1,2,-3),(0,1,2),(0,0,1)] is

Find the inverse of the matrix |[2,-1], [3, 4]| .

find the inverse of the following matrix : [{:(1,-1),(2,3):}]

Using elementary transformations, find the inverse of the matrix : [(2,0,-1),(5, 1, 0),(0, 1, 3)]

Using elementary transformation, find the inverse of the matrix ({:(2, -1, 1), (-1, 2, -1), (1, -1, 2):})

Using elementary transformation find the inverse of the matrix : A=((1, -3,2),(3, 0, 1),(-2, -1, 0))

Let A be an mxxn matrix. If there exists a matrix L of type nxxm such that LA=I_(n) , then L is called left inverse of A. Similarly, if there exists a matrix R of type nxxm such that AR=I_(m) , then R is called right inverse of A. For example, to find right inverse of matrix A=[(1,-1),(1,1),(2,3)] , we take R=[(x,y,x),(u,v,w)] and solve AR=I_(3) , i.e., [(1,-1),(1,1),(2,3)][(x,y,z),(u,v,w)]=[(1,0,0),(0,1,0),(0,0,1)] {:(implies,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. For which of the following matrices, the number of left inverses is greater than the number of right inverses ?

The number of solutions of the matrix equation X^2=[[1, 1],[ 2, 3]] is (A) more than 2 (B) 2 (C) 0 (D) 1