Question

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.

Answer 1

D=A^-1

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