I would like to display with LaTeX the start of calculation below

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A.X=0 \Longleftrightarrow\[M(A)=\left(\begin{array}{*{2}{c}}4&-2\\5&-3\\\left(\begin{array}{*{1}{c}}X\\Y\end{array} \right)\] =0 \Longleftrightarrow\begin{cases}4x-2y=0\\6x-2y=0\\\end{cases}
Could you help me solve this little problem.
Thank you!
See you soon
I tried to do. It caused a lot of bugs, I think the mix of text and number and tag issues.