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Chapter 2: Q 71E (page 100)

Question: For two invertible n 脳 nmatricesA andB , determine which of the formulas stated in Exercise 67 through 75 are necessarily true.

71.ABB鈭�1A鈭�1=In

Short Answer

Expert verified

Thus, the given equation is true.

Step by step solution

01

Use invertible matrix for the given matrices.

The given matrices are AandB which is invertible and solve the given equation as follows:

The relation of given two matrices are as follows:

AB = BA = I

Then, it is written as:

A = B-1

02

Determine the given equation of matrices is true or false.

Now, Pre-multiplication ofB-1 A-1withAB gives:

ABB鈭�1A鈭�1=ABB鈭�1A鈭�1=AIA鈭�1=AA鈭�1=I

Then, it gives ABB鈭�1A鈭�1=I.

Hence, the given equation is true.

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Most popular questions from this chapter

TRUE OR FALSE?

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