-1 Use matrix algebra to show that if A is invertible and D satisfies AD = 1, th

Question

-1 Use matrix algebra to show that if A is invertible and D satisfies AD = 1, then D =A Choose the correct answer below. OA. B. d C. D. Right-multiply each side of the equation AD=l by A-1 to obtain ADA-1-IA-1, DFA-1, and D-A-1 Add A-1 to both sides of the equation AD = l to obtain A-1 + AD-A-1 + l, ID-A-1 , and D-A-1 Left-multiply each side of the equation AD = l by A-1 to obtain A-1 AD-A-1 l, ID-A-1 , and D-A-1 . Add A-1 to both sides of the equation AD-1 to obtain AD+ A-1-l + A-1 , DI-A-1 and D-A-1

Explanation / Answer

Correct answer: C

Reason:

Remember in matrix multiplication AB is not equal to BA.

Therefore right multiplying will only give us a deadend ie

AD=I

ADA-1=IA-1

ADA-1=A-1

Now left multiplying

AD=I

A-1AD=A-1I

(A-1A)D=A-1

ID=A-1

D=A-1

Therefore proved.

Feel free to leave a comment if you have any doubts regarding this question.

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