# A dash of symmetry ......

Let $$S$$ be the set of all $$3$$x$$3$$ matrices which have only $$0$$'s and $$1$$'s as entries. (The number of entries that can be $$0$$ can be any integer from $$0$$ to $$9$$ inclusive, as is the case for the number of entries that can be $$1$$.)

The probability that a matrix, chosen at random from $$S$$, is symmetric is $$\dfrac{a}{b}$$, where $$a$$ and $$b$$ are positive coprime integers. Find $$a + b$$.

(This post was inspired by this question.)

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