# How do I invert this 3×3 matrix?

I've been following Khan Academy to try and teach myself how to invert matrices, howevever I tried to invert a 3×3 matrix and I am not sure where I have gone wrong.

I tried to invert $A$ but my answer is wrong. I would appreciate any help given.

• Your original matrix has "2" but you use "-2" in calculating the determinant! Your original matrix has "1" but you use "10" in calculating the determinant! The determinant of the matrix you show is 10, not -100. – user247327 Feb 22 '17 at 17:14
• Your mistake: You need to calculate the determinant of $A$ which is $10$. – zoli Feb 22 '17 at 17:15
• You need the determinant of the original matrix, not of the cofactor matrix. – amd Feb 22 '17 at 22:00

Note that $A$ is diagonal. Convince yourself that merely taking reciprocals of the diagonal entries yields the inverse: $$A^{-1}=\begin{bmatrix} \frac12&0&0\\ 0&\frac15&0\\ 0&0&1\end{bmatrix}$$
• @AlanPiggott It's not the determinant of $C$ you should take, it's the determinant of the original $A$. – Parcly Taxel Feb 22 '17 at 17:24
Just another note, it seems like you multiplied the central element of your matrix by $-1$ in the second line, which you're not meant to do - the diagonal elements are multiplied by $+1$ according to the Khan Academy tutorial.