Question

Question below:

Answer 1

Does exponent work the same way as in real numbers?

Answer 2

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

Answer 3

But here we have 3 terms?

Answer 4

Let AB = x
A inverse = y

Answer 5

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

Answer 6

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

Answer 7

lol

Answer 8

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

Answer 9

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

Answer 10

*searching for formulas*

Answer 11

\[(ABA^{-1})^n = (ABA^{-1})(ABA^{-1})(ABA^{-1}).... \text{n times}\]

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

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

\[~~~~~...\]

\[~~~~~= AB^nA^{-1}\]

Answer 12

matrix multiplication is associative^

Answer 13

nice!

Answer 14

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

Answer 15

np :)