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Inverse of a Matrix - Matrices and Determinants, Business Mathematics & Statistics Video Lecture | Business Mathematics and Statistics - B Com

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FAQs on Inverse of a Matrix - Matrices and Determinants, Business Mathematics & Statistics Video Lecture - Business Mathematics and Statistics - B Com

1. What is the inverse of a matrix?
Ans. The inverse of a matrix is a matrix that, when multiplied with the original matrix, yields the identity matrix. In other words, if A is a matrix and A^(-1) is its inverse, then A * A^(-1) = A^(-1) * A = I, where I represents the identity matrix.
2. How can the inverse of a matrix be calculated?
Ans. The inverse of a matrix can be calculated by using the formula A^(-1) = (1/det(A)) * adj(A), where A^(-1) represents the inverse of matrix A, det(A) is the determinant of matrix A, and adj(A) is the adjugate of matrix A.
3. Can every matrix have an inverse?
Ans. No, not every matrix has an inverse. Only square matrices, which have the same number of rows and columns, can have an inverse. A square matrix is invertible if and only if its determinant is non-zero.
4. What is the significance of the inverse of a matrix?
Ans. The inverse of a matrix is significant in various applications, such as solving systems of linear equations, calculating transformations, and finding solutions to matrix equations. It allows us to "undo" the original matrix operation.
5. Is the inverse of a matrix unique?
Ans. Yes, the inverse of a matrix is unique. If a matrix A has an inverse, it is denoted as A^(-1), and there is only one matrix that satisfies the condition A * A^(-1) = A^(-1) * A = I. If a matrix has an inverse, it is the only matrix that can be its inverse.
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