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Chapter 2: Q 72E (page 101)

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

ABA鈭�1=B

Short Answer

Expert verified

Thus, the given equation is not true.

Step by step solution

01

Use commutative laws for the given matrices.

The given matrices areA andB which is invertible and solve the given equation as follows:

Any matricesA andB that do not commute because the matrices are of order n 脳 n.

In general commutative law for multiplication do not exist that is AB鈮�BA.

02

Determine the given equation of matrices is true or false.

Post-multiplication of A-1 in the equation AB鈮�BAgives:

ABA鈭�1鈮�BAA鈭�1ABA鈭�1鈮�BIABA鈭�1鈮�B

Then it gives ABA鈭�1鈮�B

Hence, the given equation is not true.

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Most popular questions from this chapter

Which of the (nonlinear) transformations from R2toR2to in Exercises 25 through 27 are invertible? Find the inverse if it exists.25 [y1y2]=[x13x2].

IfAB=lnfor twon脳nmatrices Aand B, then Amust be the inverse of B.

TRUE OR FALSE?

If A is an invertible2脳2 matrix and B is any 2脳2 matrix, then the formula rref (AB) = rref (B)must hold.

TRUE OR FALSE?

There exists a matrix A such that[1234]A[5678]=[1111] .

TRUE OR FALSE?

The formula rref(AB) =rref(A)rref(B)holds for alln脳p matrices A and for allp脳m matrices.

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