I am new to linear algebra, and I have a rather basic question:
If I know the transformation matrix for linear transformation S ($R^3 \to R^3)$ at standard basis E (let's say it is of order 3x3) and I know the transformation matrix for linear transformation T ($R^3 \to R^3)$ at standard basis E (let's say it is also of order 3x3); can I then calculate the transformation matrix for the transformation ST at standard basis E by simply multiplying the matrix of S times the matrix of T?
In other words $[ST]_E=[S]_E·[T]_E$?
Thank you!