Let be two matrices with real entries. Prove that

provided all the inverses appearing on the left hand side exist.

*(Vojtech Jarnik / 2nd Category/ 2015)*

**Solution**

Let be elements of an arbitrary associative algebra with unit. Then:

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Let be two matrices with real entries. Prove that

provided all the inverses appearing on the left hand side exist.

*(Vojtech Jarnik / 2nd Category/ 2015)*

**Solution**

Let be elements of an arbitrary associative algebra with unit. Then: