Tackley3910 Tackley3910

17-10-2019
Mathematics

contestada

(c) Is it possible for an n × n matrix A to satisfy A3 = In without A being invertible? Explain

Respuesta :

LammettHash LammettHash

17-10-2019

If [tex]A^3=I[/tex], then [tex]A^3=AA^2=I[/tex] which means [tex]A[/tex] and [tex]A^2[/tex] must be inverses of one another, so [tex](A^2)^{-1}=A[/tex] and [tex]A^{-1}=A^2[/tex], so [tex]A[/tex] must be invertible.

Answer Link

Otras preguntas

how are new zealands major commercial industries tied to its agriculture products

Prove that: [tex]{ \left( { e }^{ \sqrt { { e }^{ \ln { \left( \frac { { 3 }^{ 0 } }{ \sin { \left( \frac { \pi }{ 2 } \right) } } \right) } } } } \righ

Why did many Americans believe imperialism was wrong?A. BECAUSE IT DESTROYED NATIVE CULTURES.B. BECAUSE IT CREATED MONOPOLIES.C.BECAUSE EUROPEAN COUNTRIES HAD C

Why has the Southeast become a center for food processing?

a local business was looking to hire a landscaper to work on their property. they narrowed their choices to two companies. flourish landscaping company charges

How do you solve this problem, it's confusing for me. Question : Kermit hopped 10 feet to the right. He then took three green power hops to the left. If the to

if an object turns but maintains the same speed,has its acceleration changed?explain

what organization was not created during the war years.?

Please help I've been stuck on this question for a while Mark the statement if it accurately describes European history and geography. A. The Alps are mountain

To get in between two people when it's not your problem or issue