The study of determinants and matrices can be confusing at time. They look almost the same, and are closely related. As such, some mathematical operations on them are similar.
But, there are differ somewhat and have to be taken care of.
Below is one such mistake that is often made by learning math students.
The upper row involves matrices. The scalar multiplication of it by "a" affects ALL the elements within the matrix.
For the lower row, the scalar "a" multiplication affects only one column (or one row) of the determinant.
Just note this different and commit it to memory. This is good for you and can save you a lot of further troubles with matrix and determinant.
So, just simply identifying the differences between matrices and determinant, in term of their operations, you will be enjoying them for a long time.
With less mistake made, you will be more gear towards doing a better job out of maths. This is human nature.
Cheers! and Happy mathematics!