Solve the matrix equation for A?

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Solve the matrix equation for A?

Mathematics
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|dw:1327007851191:dw|
Oh yay my friends are here
you need the inverse of the matrix on the left, do you know how to find that?

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I know how to do that but they want me to do a simpler method
...like what? maybe it would help if I could actually see the matrix on the right. try to use the equation feature to type it, you can make 2X2 matrices with it.
|dw:1327008078673:dw|
is the right side the identity matrix?
ya but we didnt really learn that yet. We only learnt multiplying and addition and subtraction
I can't see the matrix on the RHS is my problem what is it, the identity matrix?
Like maybe a is a 2 by 2 matrix
ohhh i see it okk i will redraw it
|dw:1327008221822:dw|
since BA=I wouldnt A=B^-1 I ?
I know but we didnt really use inverse matrices yet But if i cant solve it any other way i will do it that way
...so that is the identity matrix so we could solve this by multiplying out our matrix A with the one on the LHS and get a system of equations:\[2a_{11}-a_{21}=1\]\[3a_{11}-2a_{21}=0\]\[2a_{12}-a_{22}=0\]\[3a_{12}-2a_{22}=1\]
\[\begin{pmatrix}a&b\\c&d\end{pmatrix}^{-1}=\frac{1}{det}\begin{pmatrix}d&-b\\-c&a\end{pmatrix}\]
I only did it this way amistre because they said not to use the inverse... but yes, the inverse seems the smarter/easier way to do it.
youre way is fine, I just did that for the practice really :)
ok Thanks
also, i think the GaussJordan comes up with an inverse as well
Ya it does :D Thanks guys

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