Mathematics

Matrix addition requires matching dimensions because each element occupies a specific position—the entry in row $i$, column $j$ of one matrix must correspond to the same position in the other. A $3\times 4$ matrix has 3 rows and 4 columns, while a $4\times 3$ matrix has 4 rows and 3 columns, so their positions don't align. Having the same total count of elements is irrelevant; what matters is that the structure and indexing must be identical.

Matrix addition requires matching dimensions because each element occupies a specific position—the entry in row $i$, column $j$ of one matrix must correspond to the same position in the other. A $3\times 4$ matrix has 3 rows and 4 columns, while a $4\times 3$ matrix has 4 rows and 3 columns, so their positions don't align. Having the same total count of elements is irrelevant; what matters is that the structure and indexing must be identical.