Each of the entry selection formats described in Matrix and Vector Entry Extraction can be used on the left-hand side of an assignment statement. Entries selected in the left-hand side of the assignment statement are replaced by the corresponding entries of the right-hand side.  Unspecified entries are set to 0. The number of dimensions in such an assignment statement must match; a Vector can be assigned to a submatrix, provided it is a 1 x n submatrix.

For example, the assignment

A := Matrix([[9,9,9,9],[9,9,9,9],[9,9,9,9],[9,9,9,9]]);

$A≔\left[\begin{array}{cccc}9& 9& 9& 9\\ 9& 9& 9& 9\\ 9& 9& 9& 9\\ 9& 9& 9& 9\end{array}\right]$

A[1..2, 2..4] := Matrix([[5, 6], [7, 8]]);

$A_{1..2,2..4}≔\left[\begin{array}{cc}5& 6\\ 7& 8\end{array}\right]$

A;

$\left[\begin{array}{cccc}9& 5& 6& 0\\ 9& 7& 8& 0\\ 9& 9& 9& 9\\ 9& 9& 9& 9\end{array}\right]$

replaces A[1, 2] with 5, A[1, 3] with $6$, A[2, 2] with $7$, and A[2, 3] with $8$. The entries A[1, 4] and A[2, 4] are set to 0.

It is not necessary for the selection on the left-hand side of an assignment statement to represent contiguous nor ordered components of the Matrix or Vector. For example, A[[ 3, 1], 1..-1] := B replaces row 3 and row 1 of A with, respectively, row 1 and row 2 of some existing Matrix B.

All of the assignment operations mentioned operate in place -- the resulting Matrix or Vector overwrites the original Matrix or Vector. One consequence is that the command A[1..-1, 1..-1] := Matrix([[...], ..., [...]]) causes a replacement of all the entries of A, whereas the command A := Matrix([[...], ..., [...]]) creates a new Matrix.

For all assignments, the values on the right-hand side must be of the same or compatible datatype as that of the Matrix or Vector on the left-hand side. Furthermore, it is an error if the right-hand side does not fit into the selected submatrix, subvector, or scalar location specified on the left-hand side. It is not an error if the right-hand side is smaller than the left-hand side.