I'd argue that the Grassmann algebra is simpler than linear algebra. Deriving the determinant from its definition makes very little sense to me even today but i

I'd argue that the Grassmann algebra is simpler than linear algebra. Deriving the determinant from its definition makes very little sense to me even today but it falls out pretty naturally from the definition of wedge product, i.e. the coefficient of the highest degree wedge product. Also, a lot of the operations in geometric algebra have pretty much direct geometric analogs whereas in linear algebra you have to jump through some hoops to figure out what the formulas mean geometrically.