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Exercise - 3.4

Question-1 :-  Using elementary transformations, find the inverse , matrices

Solution :-
  In order to use elementary row operations we may write A = IA.
matrices
    

Question-2 :-  Using elementary transformations, find the inverse , matrices

Solution :-
  In order to use elementary row operations we may write A = IA.
matrices
    

Question-3 :-  Using elementary transformations, find the inverse , matrices

Solution :-
  In order to use elementary row operations we may write A = IA.
matrices
    

Question-4 :-  Using elementary transformations, find the inverse , matrices

Solution :-
  In order to use elementary row operations we may write A = IA.
matrices
    

Question-5 :-  Using elementary transformations, find the inverse , matrices

Solution :-
  In order to use elementary row operations we may write A = IA.
matrices
    

Question-6 :-  Using elementary transformations, find the inverse , matrices

Solution :-
  In order to use elementary row operations we may write A = IA.
matrices   
    

Question-7 :-  Using elementary transformations, find the inverse , matrices

Solution :-
  In order to use elementary row operations we may write A = IA.
matrices
    

Question-8 :-  Using elementary transformations, find the inverse , matrices

Solution :-
  In order to use elementary row operations we may write A = IA.
matrices
    

Question-9 :-  Using elementary transformations, find the inverse , matrices

Solution :-
  In order to use elementary row operations we may write A = IA.
matrices
    

Question-10 :-  Using elementary transformations, find the inverse , matrices

Solution :-
  In order to use elementary row operations we may write A = IA.
matrices
    

Question-11 :-  Using elementary transformations, find the inverse , matrices

Solution :-
  In order to use elementary row operations we may write A = IA.
matrices
    

Question-12 :-  Using elementary transformations, find the inverse , matrices

Solution :-
  In order to use elementary row operations we may write A = IA.
matrices
  Now, in the above equation, we can see all the zeroes in the second row of the matrix on the Left Hand Side.
  Therefore, A-1 doesn't exist. 
    

Question-13 :-  Using elementary transformations, find the inverse , matrices

Solution :-
  In order to use elementary row operations we may write A = IA.
matrices
    

Question-14 :-  Using elementary transformations, find the inverse , matrices

Solution :-
  In order to use elementary row operations we may write A = IA.
matrices
  Now, in the above equation, we can see all the zeroes in the first row of the matrix on the Left Hand Side.
  Therefore, A-1 doesn't exist. 
    

Question-15 :-  Using elementary transformations, find the inverse , matrices

Solution :-
  In order to use elementary row operations we may write A = IA.
matrices
matrices
    

Question-16 :-  Using elementary transformations, find the inverse , matrices

Solution :-
  In order to use elementary row operations we may write A = IA.
matrices
    

Question-17 :-  Using elementary transformations, find the inverse , matrices

Solution :-
  In order to use elementary row operations we may write A = IA.
matrices
    

Question-18 :-  Matrices A and B will be inverse of each other only if
(A) AB = BA   (B) AB = BA = 0   (C) AB = 0, BA = I   (D) AB = BA = I

Solution :-
  We know that if A is a square matrix of order m, and if there exists another square matrix 
  B on the same order m, such that AB = BA = I, then B is said to be the inverse of A.
  In this case, it is clear that A is the inverse of B.
  Thus, matrices A and B will be inverses of each other only if AB = BA = I.
    
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