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What is det(det(A)) ?
Det(A)=4
Which is the answer
- 4
- 16

when I think of this question I thought answer

to be 4 As det(det(A)) = det(4) { now I will treat it as a single element } = 4
But this turns out to be wrong why ?? det(det(A)) = det(A).det(A) ?

user560199
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    Of course $\det(\det(A)) = \det(A)$, so you are right. Please learn to use LaTeX formatting for your equations, because it's not clear to me what you mean by "detA.det(A)". – Michael Grant May 09 '18 at 00:03
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    $\det(\cdot)$ is a function which takes inputs from the set of square matrices and outputs a real number. If you insist on treating real numbers as $1\times 1$ matrices (which I disagree with)... then $\det(\det(A))=\det(A)$ – JMoravitz May 09 '18 at 00:04
  • I do agree with your pedantry @JMoravitz ;-) – Michael Grant May 09 '18 at 00:04
  • I have edited the Question and thanks for this but LaTex method I have no idea about this . I am in 12th grade so if you could please Answer as per my level – user560199 May 09 '18 at 02:20
  • We already did. If you are strict about what inputs are allowed, then det(det(A)) is undefined. If you treat real numbers as 1x1 matrices then det(det(A))=det(A) and so given that det(A) is four, so too is det(det(A)). Why you seem to be under the impression that it could be anything else is a mystery to me. You say "but this turns out to be wrong"... how and why do you think that? If you are looking at an answer key and the answer to the actual question is not 4 but is instead 16 then you very likely didn't ask the question correctly. – JMoravitz May 09 '18 at 06:57
  • For example, if the question were instead about finding $\det(A^2)$ that would in fact expand as $\det(A)\cdot \det(A)$ – JMoravitz May 09 '18 at 07:00

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If you have the determinant of A, you have a value of spatial scaling. The value is a real number, meaning you flatten the space into a value. If you take that value of scaling and take the value that that scales to (the determinant), you have the determinant itself.

sleepyFriend
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