Finding Inverse of Matrix using Elementary Operations

# Finding Inverse of Matrix using Elementary Operations Video Lecture | Mathematics (Maths) Class 12 - JEE

## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests

## FAQs on Finding Inverse of Matrix using Elementary Operations Video Lecture - Mathematics (Maths) Class 12 - JEE

 1. How do elementary operations help in finding the inverse of a matrix?
Ans. Elementary operations, such as row operations, can transform a matrix into its row-echelon form or reduced row-echelon form. By applying these operations to both the original matrix and the identity matrix, we can eventually obtain the identity matrix on the left side, which corresponds to the inverse of the original matrix on the right side.
 2. What are the elementary row operations used in finding the inverse of a matrix?
Ans. The elementary row operations used in finding the inverse of a matrix are: 1) Swapping two rows 2) Multiplying a row by a non-zero scalar 3) Adding a multiple of one row to another row
 3. Can any matrix have an inverse?
Ans. No, not all matrices have an inverse. A matrix is said to be invertible or nonsingular if its determinant is non-zero. Only invertible matrices can have an inverse. If a matrix is singular, meaning its determinant is zero, it does not have an inverse.
 4. What is the significance of the inverse of a matrix?
Ans. The inverse of a matrix is significant because it allows us to solve systems of linear equations, calculate the inverse of linear transformations, and perform various other mathematical operations. It acts as a counterpart to division in ordinary arithmetic.
 5. Is it possible for a matrix to have more than one inverse?
Ans. No, a matrix cannot have more than one inverse. If a matrix has an inverse, it is unique. If we assume that a matrix has two inverses, A and B, then AB = I (where I is the identity matrix) and BA = I. By multiplying both equations, we get ABA = I, which implies that A = B. Therefore, the inverse of a matrix is always unique.

## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests

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