Newton's method: matrix multiplication

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To compute an iteration of Newton's method, I need to multiply a gradient vector (G) with a hessian matrix (H).

But my hessian matrix has dimension $2\times2$ and my gradient vector dimension $2\times1$.

Since they are called vector and matrix, I guess this is correct.

But now how do I compute $G * H^{-1}$ ? Because the dimensions aren't equal?