Composition of linear mappings

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We consider the following linear mappings in the Euclidean plane $\mathbb{R}^2$ : $L_A$ is the reflection in the horizontal axis and $L_B$ is the reflection in the line $y=x$ . Consider now the linear mapping $L_C$ in which you firstly reflect in the horizontal axis and secondly reflect in the line $y=x$ .

What are the defining matrices $A$ , $B$ and $C$ ?

matrix $A={}$

$\matrix{\Box & \Box \\ \Box & \Box}$

matrix $B={}$

$\matrix{\Box & \Box \\ \Box & \Box}$

matrix $C={}$

$\matrix{\Box & \Box \\ \Box & \Box}$

Linear mappings: Linear mappings

Composition of linear mappings