here I put my answer as a picture
but some teacher said You have obviously made a mistake somewhere, either in the inverse or in your check. When you multiplied A-1 by A, you should have gotten the identity matrix I, but you didn't. That should be a clue that you've done something wrong.
please hlep me
Dear r-soy,
Yes. You have done something wrong in getting the inverse of A. Your answer is not exactly mine.
My answer: $\displaystyle A^{-1}=\left(\begin{array}{ccc}-1&1&1\\-2&3&2\\0.5&-0.25&-0.25\end{array}\right)$
Your answer: $\displaystyle A^{-1}=\left(\begin{array}{ccc}-1&1&1\\-2&3&2\\0.5&{\color{red}0.25}&-0.25\end{array}\right)$
Dear r-soy,
Please check the highlighted parts...
$\displaystyle \left(\begin{array}{ccc}-1&1&1\\-2&3&2\\{\frac{2}{4}}&{-\frac{1}{4}}&{-\frac{1}{4}}\end{array}\right)\left(\begin{array}{ ccc}1&0&4\\-2&1&0\\4&-1&4\end{array}\right)=\left(\begin{array}{ccc}1&0& 0\\0&1&0\\{\color{red}-1}&{\color{red}-\frac{2}{4}}&1\end{array}\right)$