Question

Calculate the products AB and BA to verify that B is the inverse of A.

Answer 1

Do you know how to multiply matrices? This looks like it is just matrix multiplication.

Answer 2

\[A= \left[\begin{matrix}6 & -5 \\ 1 & -1\end{matrix}\right] B= \left[\begin{matrix}1 & -5 \\ 1 & -6\end{matrix}\right]\]

Answer 3

AB = ?
BA= ?

Answer 4

who can solve it?

Answer 5

http://www.purplemath.com/modules/mtrxmult.htm

Answer 6

and please give me the equation so I can try

Answer 7

Read the link I gave. It is not a simple formula.

Answer 8

yes looks long and difficult I'll give it a try.

Answer 9

crap I don't know

Answer 10

can anyone give me the answer if possible ?

Answer 11

\[AB= \left[\begin{matrix}6 & \color\red{-5} \\ \color{blue}{1} & \color{green}{-1}\end{matrix}\right]\left[\begin{matrix}\color{teal}{1} & \color{orange}{-5} \\ \color{\pink}{1} & \color{purple}{-6}\end{matrix}\right]\]\[\qquad=\left[\begin{matrix}(6\times\color{teal}{1})+(\color\red{-5}\times\color{\pink}{1}) && (6\times \color{orange}{-5})+(\color\red{-5}\times\color{purple}{-6}) \\\\ (\color{blue}{1}\times\color{teal}{1})+(\color{green}{-1}\times\color{\pink}{1}) && (\color{blue}{1}\times \color{orange}{-5})+(\color{green}{-1}\times\color{purple}{-6})\end{matrix}\right]\]

Answer 12

okay what do I do now

Answer 13

what do I do with those number?

Answer 14

multiply

Answer 15

then add

Answer 16

okay let me try

Answer 17

you should get a nice simple matrix with four elements

Answer 18

is the answer 0 0

0 1

Answer 19

not sure if I did it right?

Answer 20

that is almost correct,

one of the elements isn't right

Answer 21

let me check again gah I hate matrix

Answer 22

1 0
0 1

Answer 23

good stuff

Answer 24

thanks Unkle so with BA what should I do for that one?

Answer 25

the opposite ?

Answer 26

now you have to calculate

\[BA= \left[\begin{matrix}\color{teal}{1} & \color{orange}{-5} \\ \color{\pink}{1} & \color{purple}{-6}\end{matrix}\right]\left[\begin{matrix}6 & \color\red{-5} \\ \color{blue}{1} & \color{green}{-1}\end{matrix}\right]\]

Answer 27

use the same method,

Answer 28

oo that's why you gave me the colors huh

Answer 29

is it the same thing as aB?

Answer 30

you are the master thank you!

Answer 31

yeah , they are the same in this case,

when AB=BA=I
the matrices A and B are inverse of one another



however in general, AB≠BA