To make your work easier to do and to read, calculate your determinants like this:
Multiply three numbers up to the right (as shown in pink), multiply three numbers up to the left (as shown in blue), then subtract the sums as shown.
You will find the work easier to do, to read, to check, and to get right. Other formats will work, yes; this is but one option. However you do your work, do it well! Create order and beauty in the world. Make a product you can be proud of. (There are times to do something quick and hurried, but those times are not all times.)
What do you do or can you think of to make your work more beautiful and efficient?