Prove that every matrix in $GL_2(\mathbb{R})$ is a product of at most 4 elementary matrices. Prove that every matrix in $GL_2(\mathbb{R})$ is a product of at most 4 elementary matrices.
$GL_2(\mathbb{R})$ = set of invertible matrices of order 2×2.
How should i approach to prove this?

Use the fact that every elementary matrix operation can be achieved by multiplying the matrix with a suitable elementary matrix, as explained here. Now how many elementary matrix operations you need to perform to bring a matrix from $GL_2(\mathbb{R})$ to an elementary matrix?
