3
QuizMultiple Choice

Matrices and Their Inverses — Quiz

Question 3 • Advanced Algebra: Concepts and Connections

If C and D are matrices and C is the inverse of D , which of the following is true?

Answer
A
cap c cap d is equal to cap d cap c is equal to cap i
B
cap c plus cap d is equal to cap d plus cap c is equal to cap i
C
cap c minus cap d is equal to cap d minus cap c is equal to cap i
D
cap c over cap d is equal to cap d over cap c is equal to cap i

Explanation

If C is the inverse of D, multiplying them in either order gives the identity matrix I: CD = I and DC = I. Therefore, the true statement is that C times D and D times C both equal I. Addition, subtraction, and division are not the defining operations for matrix inverses.

AI-written and checked against the verified answer.

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