Question

Matrix Question:

Answer 1

if a product of two matrices is the identity matrix , dosent that imply one is the inverse of the other?

Answer 2

It has something to do with the inverse matrix right?

Answer 3

Oh wait. Ok.

Answer 4

The inverse matrix would be:\[\left[\begin{matrix}-8 & 4 \\ 2& -2\end{matrix}\right]\]

Answer 5

What would I do from there?

Answer 6

\[AX=B \\ A^{-1}AX=A^{-1}B \\ X=A^{-1}B \\ since \\ A^{-1}A=I\]

Answer 7

So Would I do \[\left[\begin{matrix}-8 & 4 \\ 2 & -2\end{matrix}\right]\left[\begin{matrix}1 & 0 \\ 0 & 1\end{matrix}\right]\]?

Answer 8

yes

Answer 9

So, it would be \[\left[\begin{matrix}-8 & -2 \\ 2 & -2\end{matrix}\right]\]

Answer 10

but u forgot 1/8 out of the inverse matrix

Answer 11

1/8? Where did you get the 1/8?

Answer 12

det

Answer 13

inverse of a b
c d
is
(1/ad-bc) d -b
-c a

Answer 14

Oh ok.

Answer 15

So, would it be
\[\left[\begin{matrix}-1 & -\frac{1}{4} \\ \frac 14 & -\frac 14\end{matrix}\right]\]

Answer 16

Or would I do that with the inverse matrix?

Answer 17

wait a sec let me check it

Answer 18

\[X=A^{-1}=\left[\begin{matrix}-1 & \frac{1}{2} \\ \frac{1}{4} & -\frac{1}{4} \end{matrix}\right]\\ since \\B=I\\ a+b+c+d=-\frac{1}{2}\]

Answer 19

Oh. Ok. Thanks!

Answer 20

welcome