If one of A and B is a scalar, while the other is a matrix, then A / B is a matrix of the same size, with each element being A divided by the each entry of B, or each entry of A divided by B, depending which one is a scalar.
If both A and B are matrices, then A / B is the (numerical) solution of matrix equation X B = A. The matrix B must be an non-singular square matrix and A must have n columns. Note that X B = A is solved numerically, so the solution can only satisfy the equation approximately.
>> A = [3, 2, -5]; >> B = [1, 2, -3; 2, 1, 5; 0, -1, 3]; >> X = A / B 11 -4 16 >> X * B 3 2 -5