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$$
A =
A_{11} A_{12} A_{21} A_{22} B =
B_{11} B_{12} B_{21} B_{22}
C =
C_{11} C_{12} C_{21} C_{22} =
A_{11} B_{11} + A_{12} B_{21} A_{11} B_{12} + A_{12} B_{22} A_{21} B_{11} + A_{22} B_{21} A_{21} B_{12} + A_{22} B_{22}
Block-matrix multiplication is analogous to scalar matrix multiplication.
Rotation along rows and columns.
Submatrices are multiplied and shifted.