Showing a matrix is invertible

  • Thread starter noelo2014
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Homework Statement



let A and B be nXn invertible matrices. Show that (A.B)T is invertible by finding it's inverse

Homework Equations





The Attempt at a Solution



(A.B)T=BT.AT
 
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Answers and Replies

  • #2
CAF123
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You are looking for a matrix ##C## such that ##(AB)^{T}C = C(AB)^T = I_{n}##. The question does not say that A and B are invertible, however given that the inverse of (AB)T exists you can show that they are indeed invertible.
 
  • #3
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Sorry I left out the fact that A and B are invertible.
 
  • #4
HallsofIvy
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You have already said that [itex](AB)^T= B^TA^T[/itex]. Okay, what will get rid of that [itex]B^T[/itex] and then what will get rid of that [itex]A^T[/itex]

(Of course, you know that a matrix is invertible if and only if its determinant is not 0? And that the determinant of [itex]X^T[/itex] is the same as the determinant of [itex]X[/itex]?)
 

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