The S.O.S. Mathematics primer on matrix algebra leads off thusly:

Matrices and Determinants were dis­cov­ered and devel­oped in the eigh­teenth and nine­teenth cen­turies. Initially, their devel­op­ment dealt with trans­for­ma­tion of geo­metric objects and solu­tion of sys­tems of linear equa­tions. Historically, the early emphasis was on the deter­mi­nant, not the matrix. In modern treat­ments of linear algebra, matrices are con­sid­ered first. We will not spec­u­late much on this issue.