Matrix multiplication indicates a row-by-column multiplication, where the entries in the Xth row of A are multiplied by the corresponding entries in the Yth column of B and then adding the results.

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Constructing of 16x16 Involutory Binary Matrices of Branch Number 7

In the PDF “Algebraic Construction of 16×16 Binary Matrices of Branch Number 7 with One Fixed Point”, it was given that: ...
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How can Käsper and Schwabe's Bitsliced AES Mixcolumns work

The only way I see it possible to do the matrix-multiplication in the MixColumns operation of AES is by shifting the bits in the multiplied number, and then reduce with the polynomial if needed. ...