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I have never heard of matrix division. What is it?

Yeah me too. I'm about to ask this exact question after reading the post. I only know matrix add, subtract, and multiply.

It's to multiply a matrix by the inverse of another. There's left and right division depending on which side is inverted

There are many more matrix operations that actually exist: matrix exponential, matrix log, matrix trig functions, matrix square root, ...

E.g. exponential has an infinite series representation exp(x) = SUM_k x^k / k!: it works for matrices too, and is used

May be matrix inverse?

y = Mx

—>

x = M\y