Answer: the additive inverse of the given matrix is[tex](\begin{bmatrix} -x & 2 \ 3x & -y \end{bmatrix}).[/tex]
Step-by-step explanation: The additive inverse of a matrix is the matrix that, when added to the original matrix, results in the zero matrix. Let’s find the additive inverse of the given matrix[tex](\begin{bmatrix} x & -2 \ -3x & y \end{bmatrix}).[/tex]
To find the additive inverse, we negate each element of the matrix. So the additive inverse of the given matrix is:
[tex][ \begin{bmatrix} -x & 2 \ 3x & -y \end{bmatrix} ][/tex]
Remember that the sum of a matrix and its additive inverse is always the zero matrix. In other words:
[tex][ \begin{bmatrix} x & -2 \ -3x & y \end{bmatrix} + \begin{bmatrix} -x & 2 \ 3x & -y \end{bmatrix} = \begin{bmatrix} 0 & 0 \ 0 & 0 \end{bmatrix}[/tex]
correct me if im wrong & hope this helps ^^