Sometimes, you want to apply two, or a series, of linear transformations to a grid, or vector. The end result is, in itself, a matrix, which is represented by the ending positions of î and ĵ. You can end up at the final matrix of î and ĵ (or the final vector) by multiplying the matrix of the first transformation and the second transformation.
Connections
Scaling Means To Multiply A Vector
Link Explanation: Note that scaling a vector is not exactly the same as multiplying two matrices. I could see how these get confused though. Scaling means to multiple a vector by a value. This stretches the vector itself, but does not change the basis vectors. Matrix, instead, represents the ending position of the basis vectors after a shift or flip (linear transformation) has been applied to the span (entire grid space). Mutliplying a matrix by another matrix then, represents the basis vector position after two distinct linear transformations on the original grid.
Reference
https://www.youtube.com/watch?v=XkY2DOUCWMU&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab&index=4