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Chapter 7: Q44E (page 338)

Do there exist invertiblematrices A and B such thatAB-BA=A?Explain.

Short Answer

Expert verified

Do there exist invertible.

AB-BA=AAB=A+BA=ln+BAABA-1=ln+B

Hence,

No

Step by step solution

01

definition of matrix

A function is defined as a relationship between a set of inputs that each have one output.

Given,

Assume that such matrices A and B exist.

AB-BA=AAB=A+BA=ln+BAABA-1=ln+B

02

definition of ln+B

This means thatln+B and B are similar, so they have the same trace.

Thus,

trln+B=trBtrln+trB=trBn=0

This is a contradiction. So, such matrices and do not exist.

Hence, No

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