Multiply row of the first by column of the second. Inner sizes must match: 2×3 times 3×4 works; 2×3 times 2×3 does not. Matrices as a set are in matrices.
Row times column
Addition is entry by entry and is a different leftover, in matrix addition. The inverse of a 2×2 is another leftover, in inverse of a 2×2 matrix.
The bottom line
Inner dimensions match, then row-dot-column. Do not add the entries.
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