Invertible Matrices

# Invertible Matrices Video Lecture | Mathematics (Maths) Class 12 - JEE

## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests

## FAQs on Invertible Matrices Video Lecture - Mathematics (Maths) Class 12 - JEE

 1. What is an invertible matrix?
Ans. An invertible matrix, also known as a non-singular matrix, is a square matrix that has an inverse. It means that it can be multiplied by another matrix to yield the identity matrix.
 2. How can I determine if a matrix is invertible?
Ans. To determine if a matrix is invertible, calculate its determinant. If the determinant is non-zero, then the matrix is invertible. If the determinant is zero, then the matrix is not invertible.
 3. What is the significance of invertible matrices in linear algebra?
Ans. Invertible matrices are significant in linear algebra as they allow for the solution of systems of linear equations. If a coefficient matrix of a system is invertible, then the system has a unique solution. Invertible matrices also have various applications in areas such as cryptography and computer graphics.
 4. Can a matrix be invertible if it has zero entries?
Ans. No, a matrix cannot be invertible if it has zero entries. An invertible matrix must have a non-zero determinant, which means it cannot contain any zero entries. If a matrix has at least one zero entry, its determinant will be zero, and it will not have an inverse.
 5. How can I find the inverse of a matrix?
Ans. To find the inverse of a matrix, use the formula A^(-1) = (1/det(A)) * adj(A), where A^(-1) is the inverse matrix, det(A) is the determinant of A, and adj(A) is the adjugate matrix of A. Calculate the determinant and adjugate matrix of the given matrix, then multiply the adjugate matrix by (1/det(A)) to obtain the inverse matrix.

## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests

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