To check whether the matrix B is an inverse of matrix A, we need to check whether
An n×n matrix A is said to be invertible if there exists an n×n matrix B such that AB=I, and BA=I, where I is the n×n identity matrix.
If such a matrix B exists, then it is known to be unique and called the inverse matrix of A, denoted by A^{−1}.
The inverse of a matrix is defined for
The inverse exists only for square matrix. However this is not true. A nonsingular matrix must have their inverse whether it is square or nonsquare matrix.
The inverse of is
A = IA
AA^{-1} = I
A = {(1,0),(-1,1)}
A^{-1}{(1,0),(-1,1)} = {(1,0),(0,1)}
R2 ----> R2 + R1
A^-1 {(1,0),(0,1)} = {(1,0),(1,1)}
I A^{-1} = {(1,0),(1,1)}
Therefore, A^{-1} = {(1,0),(1,1)}
The inverse of is
A = {(0,1) (1,0)}
Adj(A) = {(0,(-1)) ((-1),0)}
|A| = (0 - 1) = -1
A^{-1} = adj(A)/|A|
= -1{(0,(-1)) ((-1),0)}
= {(0,1) (1,0)}
If a matrix B is obtained from matrix A by an elementary row or column transformation then B is said to be ______ of A
ANSWER :- a
Solution :- Matrix equivalence is an equivalence relation on the space of rectangular matrices.
For two rectangular matrices of the same size, their equivalence can also be characterized by the following conditions
The matrices can be transformed into one another by a combination of elementary row and column operations.
If a matrix B is obtained from matrix A by an elementary row or column transformation then B is said to be equivalent of A.
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