It is very often that we come across the word determinant in matrices. Yes, they are related.
Matrix consists a set of numbers. That's it.
Determinant is a numerical value obtained throught the numbers within the matrix.
For a 3 x 3 matrix, how then do we extract the determinant?
One of the easiest method to obtain this number is throught the use of Rule of Sarrus.
Below I show the steps.
Determinant A = [(aei) + (bfg) + (cdh) ] - [ (gec) + (hfa) + (idb) ].
The important step lies with getting the first left 2 columns out to the right of the determinant.
After which, we do a downwards grouping and addition.
This is followed by upwards grouping with addition again.
Note, the last step is to SUBTRACT the two groups obtained above.
(By grouping, I mean to MULTIPLY the individual elements).
1) The grouping is done by "adding" instead of multiplying the elements.
2) The slanted operations (the 3 element-multiplication) are done by "adding" instead of multiplying the 3 elements.
3) The two big groups are "added" instead of subtracted".
Just bear in mind the 3 common mistakes above and you are on the way to a happy matrix student...