The spelling Hessian's is a possessive (has an apostrophe S).
You would use this to describe a Hessian, such as a Hessian's uniform.

The plural of Hessian is Hessians.

The cast of Hessians MC - 2005 includes: Hessian Animal as himself Hessian Big Dog as himself Hessian Byron as himself More Hessians as Themselves Hessian Keith as himself Hessian Leaky as himself Hessian Rtd as himself Hessian Sam as himself Hessian Smokey as himself Hessian Spike as himself

The Hessian was created in 1972.

relationship between determinant and adjoint

A single math equation does not have a determinant. A system of equations (3x3 , 4x4, etc.) will have a determinant. You can find a determinant of a system by converting the system into a corresponding matrix and finding its determinant.