It is known that the set of all $n\times n$ positive matrices $\mathbb{P}_n$ is a gyrocommutative gyrogroup by the operation $A\oplus B=A^{\frac{1}{2}}BA^{\frac{1}{2}}$. In this talk, we define a gyrogroup operation $\oplus'$ on the set of all $n\times n$ invertible matrices $\mathbb{M}_n^{-1}$. The operation $\oplus'$ is a extension of $\oplus$, that is, $\oplus'=\oplus$ on $\mathbb{P}_n$. The gyrogroup $(\mathbb{M}_n,\oplus')$ is not gyrocommutative.