Finding Invariant Line equation

[chrome hearth]

I got uptil -3mx=m(-3x) but unsure why this makes the judgement that m=+-1, I know other values don't work but why?

[torpid sequoia]

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[quartz verge]

Yeah, this is a bit odd. Any value of m should work. After all, T = 3I. It just scales everything by a factor of 3, so any line passing through the origin is invariant.

[chrome hearth]

So the question answer is incorrect?