Question: Let A and B be invertible n n matrices. Evaluate: det(A-1B-1AB)

Let A and B be invertible n × n matrices. Evaluate:
det(A-1B-1AB)

Step by Step Solution

★★★★★

3.55 Rating (148 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

det A 1 B 1 AB detA 1 detB 1 detA detB 1 detA 1 ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Document Format (1 attachment)

Word file Icon

950-M-L-A-L-S (6328).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

Let a and b be positive numbers with a > b. Let a1 be their arithmetic mean and b1 their geometric mean: Repeat this process so that, in general (a) Use mathematical induction to show that an > an+1...

Q:

Let A and B be n ( n orthogonal matrices. (a)Prove that A (AT + BT)B = A + B. (b)Use part (a) to prove that, if det A + det B = 0, then A + B is not invertible.

Q:

Let A and B be orthogonally diagonalizable n ( n matrices and let c be a scalar. Use the Spectral Theorem to prove that the following matrices are orthogonally diagonalizable: (a) A + B (b) cA (c) A2

Q:

Math for Econ II, Written Assignment 3 (28 points) Due Monday, July 24, in class Summer 2017 Please write neat solutions for the problems below. Show all your work. If you only write the answer with...

Q:

Let A and B denote invertible n x n matrices. (a) If A-1] = B], does it mean that A = P? Explain. (b) Show that A = B if and only if A-1B = I.

Q:

Let A and B be invertible n x n matrices. Find a formula for A_1 in terms of B if (BATE I)_1 = (A'lB)T. Your formula for 241 should be simplied and should not depend on A

Q:

MATH-UA.212 Written HW5 Write full, clear solutions to the problems below. It is important that the logic of how you solved these problems is clear. Although the final answer is important, being able...

Q:

MATH-UA.212 Written HW5 Write full, clear solutions to the problems below. It is important that the logic of how you solved these problems is clear. Although the final answer is important, being able...

Q:

MATH-UA.212 Written HW5 Write full, clear solutions to the problems below. It is important that the logic of how you solved these problems is clear. Although the final answer is important, being able...

Q:

Justify your answer. (T/F) If A and B are invertible n n matrices, then AB is similar to BA.

Q:

How is an aged accounts receivable trial balance prepared, and what is it used for?

Q:

Strategy usually includes some formal processes. REQUIRED 1. How can managers choose between different strategies? 2. How is strategy different from an operating decision?

Q:

You want to earn a nominal rate of return of 6 . 4 8 percent at a time when the inflation rate is 2 . 8 4 percent. What is the approximate real rate of return you must earn?Group of answer choices 3...

Q:

From the materials in this chapter, and your own experience, describe how you think CoPs might change project management practice in the future, and discuss what types of value may be created.

Q:

Set A = rand(8, 4) * rand(4, 6), [U, D, V]= svd(A) (a) What is the rank of A? Use the column vectors of V to generate two matrices V l and V2 whose columns form orthonormal bases for R(AT) and N(A),...

Q:

With each A RnÃn we can associate n closed circular disks in the complex plan. The ith disk is centered at aij and has radius Each eigenvalue of A is contained in at least one of the disks. If...

Q:

Construct a matrix C as follows. Set A = round(100 * rand(4)) L = tril(A,-1) + eye(4) C = L*L The matrix C is a nice matrix in that it is a symmetric matrix with integer entries and its determinant...

Q:

Select all scenarios where you would rate Instruction Following ( not Truthfulness ) as having issues. Think carefully! A link in the response is broken. Information within the response text does not...

Q:

Amortization 10. You have just bought a house and have a $125,000, 25-year mortgage with a fixed interest rate of 8.5 percent with monthly payments. Over the next five years, what percentage of your...

Q:

Currently struggling on a lecture problem, please explain thoroughly if possible, thank you for your help! Problem 2: Suppose you have a RNG that produces a pseudo- random sequence contained in the...