Use matrix algebra to show that if A is invertible and D satisfies ADequalsI , then Upper D equals Upper A Superscript negative 1. Choose the correct answer below. A. Left-multiply each side of the equation ADequalsI by Upper A Superscript negative 1 to obtain Upper A Superscript negative 1ADequalsUpper A Superscript negative 1I , IDequalsUpper A Superscript negative 1 , and DequalsUpper A Superscript negative 1. B. Add Upper A Superscript negative 1 to both sides of the equation ADequalsI to obtain Upper A Superscript negative 1plusADequalsUpper A Superscript negative 1plusI , IDequalsUpper A Superscript negative 1 , and DequalsUpper A Superscript negative 1.

Question

Mathematics

Dominic Thomas

23 July, 05:32

Use matrix algebra to show that if A is invertible and D satisfies ADequalsI , then Upper D equals Upper A Superscript negative 1. Choose the correct answer below. A. Left-multiply each side of the equation ADequalsI by Upper A Superscript negative 1 to obtain Upper A Superscript negative 1ADequalsUpper A Superscript negative 1I , IDequalsUpper A Superscript negative 1 , and DequalsUpper A Superscript negative 1. B. Add Upper A Superscript negative 1 to both sides of the equation ADequalsI to obtain Upper A Superscript negative 1plusADequalsUpper A Superscript negative 1plusI , IDequalsUpper A Superscript negative 1 , and DequalsUpper A Superscript negative 1.

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Answers (1)

Know the Answer?

Leonard Haynes · Answer 1

D=A^-1

Step-by-step explanation:

Given that A is invertible and matrix D satisfies AD=I

Where I is an identity matrix

D is the inverse of A

Multiply both sides of AD=I by A^-1

A^-1 (. AD) = A^-1 I

A^-1. A=I

Therefore D=A^-1