Why can't we multiply matrices entrywise? Why can't we multiply corresponding elements like addition is done?
Is there a specific reason why it won't be significant? 
By definition, we have to multiply a row by columns.
Why such a definition other than multiplying corresponding elements?
Please ignore my ignorance. I had nowhere to ask. :(

You can do such element-wise multiplication of matrices, but it obviously represents a different kind operation. The 'standard' way of multiplying matrices has important applications in linear algebra and, as such, in many areas of science and engineering. The element-wise multiplication has other (typically less used) practical applications.
