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Exercise - 3.4

Matrices

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

In order to use elementary row operations we may write A = IA.

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

In order to use elementary row operations we may write A = IA.

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

In order to use elementary row operations we may write A = IA.

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

In order to use elementary row operations we may write A = IA.

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

In order to use elementary row operations we may write A = IA.

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

In order to use elementary row operations we may write A = IA.

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

In order to use elementary row operations we may write A = IA.

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

In order to use elementary row operations we may write A = IA.

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

In order to use elementary row operations we may write A = IA.

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

In order to use elementary row operations we may write A = IA.

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

In order to use elementary row operations we may write A = IA.

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

In order to use elementary row operations we may write A = IA. 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 ,

In order to use elementary row operations we may write A = IA.

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

In order to use elementary row operations we may write A = IA. 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 ,

In order to use elementary row operations we may write A = IA.

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

In order to use elementary row operations we may write A = IA.

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

In order to use elementary row operations we may write A = IA.

**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

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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