Ask your own question, for FREE!
Mathematics 15 Online
OpenStudy (aravindg):

Question below:

OpenStudy (aravindg):

OpenStudy (aravindg):

Does exponent work the same way as in real numbers?

hartnn (hartnn):

\(\large [xy]^* = y^*x^*\)

OpenStudy (aravindg):

But here we have 3 terms?

hartnn (hartnn):

Let AB = x A inverse = y

OpenStudy (aravindg):

Then why A^-n doesnt come in first place in any of the options?

hartnn (hartnn):

woah! is the exponent = n !! i thought its * :P

OpenStudy (aravindg):

lol

hartnn (hartnn):

i guess, you can just replace * by n :P

OpenStudy (aravindg):

why A^-n doesnt come in first place in any of the options?

hartnn (hartnn):

*searching for formulas*

ganeshie8 (ganeshie8):

\[(ABA^{-1})^n = (ABA^{-1})(ABA^{-1})(ABA^{-1}).... \text{n times}\] \[~~~~~= (AB(A^{-1}A)BA^{-1})(ABA^{-1}).... \text{n times}\] \[~~~~~= (AB^2A^{-1})(ABA^{-1}).... \text{n times}\] \[~~~~~...\] \[~~~~~= AB^nA^{-1}\]

ganeshie8 (ganeshie8):

matrix multiplication is associative^

hartnn (hartnn):

nice!

OpenStudy (aravindg):

Oh!! I remember this technique ..I did a similar problem before. Thank you!

ganeshie8 (ganeshie8):

np :)

Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!
Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!