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There are a number of basic operations that can be applied to modify matrices, called matrix addition, scalar multiplication, transposition, matrix multiplication, row operations, and submatrix.
+ = = {\displaystyle {\begin{bmatrix}1&3&1\\1&0&0\end{bmatrix}}+{\begin{bmatrix}0&0&5\\7&5&0\end{bmatrix}}={\begin{bmatrix}1+0&3+0&1+5\\1+7&0+5&0+0\end{bmatrix}}={\begin{bmatrix}1&3&6\\8&5&0\end{bmatrix}}}
This operation is called scalar multiplication, but its result is not named "scalar product" to avoid confusion, since "scalar product" is sometimes used as a synonym for "inner product".
Familiar properties of numbers extend to these operations of matrices: for example, addition is commutative, that is, the matrix sum does not depend on the order of the summands: A + B = B + A. The transpose is compatible with addition and scalar multiplication, as expressed by = c and = A + B. Finally, = A.