Hus, D satisfying (ABC)DequalsI exists. Why does the expression for D found above also satisfy D(ABC)equalsI, thereby showing that ABC is invertible? Select the correct choice below and, if necessary, fill in the answer box within your choice. A. After substituting the expression for D, the product DABC simplifies to I by repeated application of the associative property and the definition of inverse matrices. B. After substituting the expression for D, left multiplying the product by nothing results in the equation IequalsABCD. C. After substituting the expression for D, taking the inverse of both sides of the equation results in the equation IequalsABCD. D. After substituting the expression for D, right multiplying the pr

Complete Question

The complete question is shown on the first uploaded image

First Question

Option A is correct

Second  Question

Option C is correct

Third   Question

Fourth   Question

  So substituting for D in  (ABC) D =  I

This proof that  ABC is invertible

Step-by-step explanation:

From the question we are told that

   A , B and  C are invertible which means that exist

Now

 From the question

          (ABC) D =  I

Where I is an identity matrix

   Now when we multiply both sides by    we have

Now when we multiply both sides by    we have  

Now when we multiply both sides by    we have  

So substituting for D in the above equation

This proof that  ABC is invertible

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step-by-step explanation: