One determinent question to prove by using properties

Question

My question is to prove a determinent by properties. 

Answer 1

This is not really a question; you don't give a problem (no specifics are given).

 

I can add, however, that a determinant (note correct spelling) is a square array of numbers having a single value.

 

For a 3 by 3 determinant, there are seven well known ways to compute this value:

three by expansion by a row, and three by expansion by a column, and one by Sarrus's method, where you replicate the first two columns, appending them to the right side of the array, multiply down diagonals, summing three products of the top to bottom, Left to Right diagonals, and then subtracting the sum of the products down the 'reverse diagonals).