how to prove that det(adj(A))=(det(A))^n-1?

[@meliemelie9085]

Very clear thank you, this helped me with my final exam in linear algebra 7 years after this video was posted !

[@themathinstructor]

Melie Melie I am glad this video helped you...

[@mohammadobeidat4504]

how about when the matrix A is singular?

[@jeannettepinzon8817]

My life have been saved, thank you!

[@thewordsmithsmysterious8503]

Nice explanations ❣️

[@biancabadescu1161]

finally someone capable of explaining how do you transform det(detA*I) in det(a)n thank you man my bro

[@rakabadi]

The best explanation online.
thank you!

[@seewhatseeabc]

holyshit

[@kaneki3614]

Bro ur video helped me even after 8 years ❤️

[@wengjunfoong815]

thanks a lotsss, you help me gain a different insight in matrix!!!!

[@MyJosef10]

This is great and really helped me figure out a problem, thanks! Very clearly done!

[@mohammedhajomar4400]

Thank you bro I used this proof for my linear alg quiz, it was so helpful. continue

[@Esmegmor]

A very clear explanation, thanks!

[@KurtAhmetErek]

Its very good. Thanks

[@hascuhas]

Great explination, thank you!

[@hihello-sk5ql]

Is this only for square matrixes

[@wafateach3910]

This is very helpful. Thank you 👍

[@Neroner94]

Thanks man!! Very good explanation!

[@zamalambulazyma6270]

Wow simply and straight Thanx

[@jerrerock]

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[@cylau5171]

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[@muu0906]

Thank U so much for have been made this video!

[@mjparker5]

This was so helpful! thanks!

[@MrTonyMaroni]

So helpful! Thanks!

[@thuanh1153]

Can u prove that |detA| = 1 with A invertible?

[@rabiaghaly3543]

Thank you very much

[@로욜라-n5v]

OMG It was really helpful. Thanks!

[@nazanintabrizizadeh72]

thank you so much.

[@daw1518]

You are God, thanks for share this video (Y)

[@patrickrogers2452]

Thanks so much!

[@BlueMarble22]

Thank you.

[@beatrice5108]

awesome thank you lots

[@ImranKhan-kh7jx]

thank you

[@derdiplomat5467]

what if a isn´t invertable

[@eminedemir8708]

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[@sanketgautam4015]

Thanku if you are still reading the comments after 7 years

[@mysterynadi]

a step by step explanation , thank you! deserved the 0 dislikes xD

[@ekao9187]

tx bruv

[@snaildude268]

Thank youu

[@Panchoyz]

muy bueno gracias

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Obrigado

[@mxngxrx]

Thanks!!!!!

[@OCEVNMusic]

thanks

[@julialocamuz7164]

thanks!!!

[@yuvaliko]

amazing! thanks

[@artority]

How about this case ; detA is 0

[@MuffinsAPlenty]

A·adj(A) = adj(A)·A = det(A)·I is a true statement _regardless_ of what det(A) is. So you can still use this fact for the case that det(A) = 0.
Suppose det(A) = 0. This has two subcases.
If A is not the 0 matrix, then adj(A)·A = det(A)·I = 0·I = 0. Since adj(A) multiplies a nonzero matrix to 0, then adj(A) is _not_ invertible. Hence, det(adj(A)) = 0.
If A is the 0 matrix, then it's easy to see using the definition of adj(A) that adj(A) is the 0 matrix too. So of course, det(adj(A)) = 0 in this case.
And of course, 0 = 0^(n-1) (when n is at least 2).

[@jayaseelana4663]

det(adj(adj(a)))=(det(a))^(n-1)^2 can U pls prove this..

[@MuffinsAPlenty]

Let B = adj(A).
det(adj(B)) = det(B)^(n-1) (by the proof shown in this video).
det(B) = det(adj(A)) = det(A)^(n-1)
Substitute into the previous line
det(adj(B)) = (det(A)^(n-1))^(n-1) = det(A)^((n-1)(n-1)) = det(A)^((n-1)^2)

[@ahmarajeel]

thanks man!

[@nightmare_9.11]

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[@vipingupta1192]

If det(A)=0 then

[@MuffinsAPlenty]

A·adj(A) = adj(A)·A = det(A)·I is a true statement _regardless_ of what det(A) is. So you can still use this fact for the case that det(A) = 0.
Suppose det(A) = 0. This has two subcases.
If A is not the 0 matrix, then adj(A)·A = det(A)·I = 0·I = 0. Since adj(A) multiplies a nonzero matrix to 0, then adj(A) is _not_ invertible. Hence, det(adj(A)) = 0.
If A is the 0 matrix, then it's easy to see using the definition of adj(A) that adj(A) is the 0 matrix too. So of course, det(adj(A)) = 0 in this case.
And of course, 0 = 0^(n-1) (when n is at least 2).

[@DANIELMARTINEZ-ov5ml]

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[@nightmare_9.11]

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[@两根发菜]

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[@nachogamer4212]

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[@tuananhnguyenvuong2245]

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