Matrix addition and subtraction are performed element-wise. This means that the corresponding elements in each matrix are added or subtracted to form the elements of the resulting matrix.

Requirement:

For these operations to be possible, both matrices must have the exact same dimensions (the same number of rows and columns).

Formula:

For two matrices A and B of size \(m \times n\), the resulting matrix \(C = A + B\) is defined as:

\(C_{ij} = A_{ij} + B_{ij}\)

Similarly, for subtraction \(D = A - B\):

\(D_{ij} = A_{ij} - B_{ij}\)