Question

if A is a 3-rowed square matrix such that |A|=2 then \[\large |adj(adj A^2)|=?\]

Answer 1

This might help: http://mathinstructor.net/2012/04/how-to-prove-that-adjadja-a-deta-power-n-2/

Answer 2

oh!!thanks that is what i was looking for thats a short cut way
unless it is getting too messy

Answer 3

I've never seen this before, I've not played with adjoints of matrices past the common identity for finding the inverse of a matrix: \[\LARGE A^{-1}=\frac{adj(A)}{\det(A)}\]

Answer 4

yeah it a good kinda brain teaser
so i have to use this
\[\large |adj(adj A^2)|=|A^2|^{{(n-1)}^{2}}\]

Answer 5

Yep and then the final thing is really just to note that: \[\LARGE \det(A^p)=(detA)^p\] which is super handy.

Answer 6

because
\[|adj(adj A)|=|A|^{{(n-1)}^2}\]

Answer 7

yep thanks for this priceless formula :P

Answer 8

so my answer will be \[\Large A^8\]
right?

Answer 9

|A|^8 = 256 :)

i think the previous formula follows from :
\[\large |adj(A)| = |A|^{n-1}\]

Answer 10

means 2^(8)
yeah

Answer 11

which follows from :
\[\large A(adj(A) = |A|I\]

Answer 12

yep
\[A(adjA)=|A|I\]

Answer 13

thanks @Kainui and @ganeshie8 :)