SOLUTION: Que:If A is an invertible matrix of order 2,then det(A^(-1)) is equal to ? My solution: {{{A^(-1)=(1/|A|)*(adj(A))}}} So, |A^(-1)|={{{|(1/|A|)*(adj(A)|}}} ={{{|

Algebra ->  Matrices-and-determiminant -> SOLUTION: Que:If A is an invertible matrix of order 2,then det(A^(-1)) is equal to ? My solution: {{{A^(-1)=(1/|A|)*(adj(A))}}} So, |A^(-1)|={{{|(1/|A|)*(adj(A)|}}} ={{{|      Log On


   

Question 187223: Que:If A is an invertible matrix of order 2,then det(A^(-1)) is equal to ?
My solution:
A%5E%28-1%29=%281%2F%7CA%7C%29%2A%28adj%28A%29%29
So, |A^(-1)|=%7C%281%2F%7CA%7C%29%2A%28adj%28A%29%7C
=%7C%281%2F%7CA%7C%29%7C%2A%7C%28adj%28A%29%29%7C
=%281%2F%7C%7CA%7C%7C%29%2A%7CA%7C%5E%28n-1%29
=%7CA%7C%5E%28n-1%29%2F%28%7CA%7C%29
Given order =2
=>|A^(-1)|=%7CA%7C%2F%7CA%7C=1
Answer given at the back of the textbook is 1/|A|
How to arrive at such a result?

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Your post was completely gargled.
Cheers,
Stan H.