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(A-¹) = (A¹) (assuming A- exists) (AB)−¹ = B¯¹A−¹ (assuming A-¹ and B-¹ exist)

(A-¹) = (A¹) (assuming A- exists) (AB)−¹ = B¯¹A−¹ (assuming A-¹ and B-¹ exist)

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Using the definition of an inverse, show that matrix inversion obeys

The image contains two mathematical expressions related to matrix operations, specifically involving transposes and inverses. Here is the transcription and explanation: 1. \((A^{-1})^{\top} = (A^{\top})^{-1}\) This expression states that the transpose of the inverse of a matrix \(A\) is equal to the inverse of the transpose of the matrix \(A\). This holds true assuming that the inverse of matrix \(A\) exists. 2. \((AB)^{-1} = B^{-1}A^{-1}\) This expression indicates that the inverse of the product of two matrices \(A\) and \(B\) is equal to the product of the inverses of \(B\) and \(A\), but in reverse order. This is valid assuming the inverses of both matrices \(A\) and \(B\) exist.
Transcribed Image Text:The image contains two mathematical expressions related to matrix operations, specifically involving transposes and inverses. Here is the transcription and explanation: 1. \((A^{-1})^{\top} = (A^{\top})^{-1}\) This expression states that the transpose of the inverse of a matrix \(A\) is equal to the inverse of the transpose of the matrix \(A\). This holds true assuming that the inverse of matrix \(A\) exists. 2. \((AB)^{-1} = B^{-1}A^{-1}\) This expression indicates that the inverse of the product of two matrices \(A\) and \(B\) is equal to the product of the inverses of \(B\) and \(A\), but in reverse order. This is valid assuming the inverses of both matrices \(A\) and \(B\) exist.
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