Where did block matrix multiplication appear?

I am curious about who first noticed that block matrices can be multiplied blockwise.

There is a section about matrices partitioned into submatrices that describes block matrix multiplication in "An introduction to the theory of canonical matrices" by Turnbull and Aitken, but there are earlier references that use block matrices and their multiplication and inverses, for example, Schur's dissertation "Über eine Klasse von Matrizen...". A natural guess for the origin of block matrices would be Jordan's "Traité des substitutions et des équations algebriques", but it seems from the formulas that Jordan does not employ block matrices and I don't read French, so I cannot say if Jordan mentions something in text.

Is there a reference earlier that Turnbull–Aitken that talks explicitly about multiplication of block matrices or was it a folklore simple thing?