Matrices and Determinants: JEE Main 2021 Mathematics question

If $\alpha$ + $\beta$ + $\gamma$ = 2$\pi$, then the system of equations x + (cos $\gamma$)y + (cos $\beta$)z = 0 (cos $\gamma$)x + y + (cos $\alpha$)z = 0 (cos $\beta$)x + (cos $\alpha$)y + z = 0 has :