How do I convert a matrix, or just 3 vectors, into a rotation vector?

If I have a matrix where the x, y, and z vectors are all perpendicular to
each other, and left-handed, and there's no translation, how do I find out
which rotate statement will transform my object in the same way as the
matrix?

For example

matrix <0,0,-1,0,1,0,1,0,0,0,0,0>

will produce the same result as

rotate <0,90,0>

I need a function that can convert any matrix (or just 3 vectors) that
follows the requirements into a rotate vector. How could that be done? Is it
possible at all?

Greetings,

Rune

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