The following table can be completed is just one way to make

The following table can be completed is just one way to make * associative. Find this completion. (You do not need to verify that the resulting operation is associative.)

Solution

0 * ( 0 * 2 ) = ( 0 * 0 ) * 2

=> 0 * ( 0 * 2 ) = 0 * 2

=> 0 * 2 = 2

2 * ( 1 * 1 ) = ( 2 * 1 ) * 1

=> 2 * 1 = ( 2 * 1 ) * 1

=> 2 * 1 = 2

Hence , both blanks need to be filled by 2