Why I can't find inverse of matrix 2x2 by 3x3 method?

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I was trying to find 2x2 matrix inverse by folllowing 3x3 matrix inverse tutorial. I had understood 3x3 matrix inverse but I couldn't use 3x3 system in 2x2.

$$A=\begin{bmatrix}7 & 2 \\ 17 & 5\end{bmatrix}$$

It's the given matrix. So I am going to find det of it.

$$|A|=\det A=1$$

$$A^{-1}=\frac{1}{1}\begin{bmatrix}+|5| & -|17| \\ +|2| &-|7|\end{bmatrix}$$ $$=\begin{bmatrix}5 & -17 \\ 2 & -7\end{bmatrix}$$

I thought it was correct answer. So I was trying to check validity by multiplying A and $A^{-1}$ after multiplying them I noticed my answer was incorrect. What I missed here? I had rechecked my work either but couldn't find any mistake. I was just following his hiding variable method (I have added the accurate time). From the following equation I found that his method isn't helpful for 2x2 matrix. Or I understood his method wrong for 2x2 matrix.