Using connectedness of $SL_n(R)$ How to show that $Gl_n(R)^+$ is connected?

Question

Using connectedness of $SL_n(R)$ How to show that $Gl_n(R)^+$ is connected?

I can prove that Sl_n(R) is connected . How to prove using this fact only connectedness of all matrices with positive determinant ?

I wanted to solve this problem. Please give me hint.

Answer 1

Hint: $GL_n(\mathbb R)^+ = \mathbb R^+ \cdot SL_n(\mathbb R)$.