If $ \ S : \mathbb{R}^3 \to \mathbb{R}^3 \ $ be a shear map with respect to the unit vector $ \ n \ $ Select the correct options : (1) If $ \ S : \mathbb{R}^3 \to \mathbb{R}^3 \ $ be a shear map with respect to the unit vector $ \ n \ $ , then $ \ S (x)=x \ $ for every $ \ x \perp n \ $ (2) If $ \ S : \mathbb{R}^3 \to \mathbb{R}^3 \ $ be a shear map with respect to the unit vector $ \ n \ $ , then $ \ || S (x)|| =||x|| \ $ for every $ \ x \perp n \ $ (3) If $ \ S : \mathbb{R}^3 \to \mathbb{R}^3 \ $ be a shear map with respect to the unit vector $ \ n \ $ , then $ \ S (x)=x \ $ for every $ \ x \in \mathbb{R}^3 \ $ **Answer:** We know that a **shear map** shift a vector along a particular direction. But I can not answer the above questions. Can some one help me with atleast hints?

**HINT**

In the basis $\\{m_1,n,m_2\\}$ with $m_1\perp n$ and $m_2\perp n,m_1$ we have that

$$T_S=\begin{bmatrix}1&k&0\\\0&1&0\\\0&0&1\end{bmatrix}$$