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How do I prove the set of non-invertible matrices is unbounded?

Attempt:

Let A be an element of set of non-invertible matrices.

det(A)=0

det(A)=0 is just the line y=0 if you have det(A) as the y-axis and the set of non-invertible matrices on the x-axis. y=0 is unbounded, so the set of non invertible matrices is unbounded?

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# Set of non-invertible matrices is unbounded

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