### Composition and Matrix Multiplication

Exercise Draw the picture and identify the composition `TS`.

1) **T** = `Reflection in x-axis`: **R**^{2} → **R**^{2}

**S** = `Reflection in y-axis`: **R**^{2} → **R**^{2}

Answer The composition `TS` is `Reflection in origin`: **R**^{2} → **R**^{2}

2) **T** = `Rotation by 90 degrees`: **R**^{2} → **R**^{2}

**S** = `Reflection in origin`: **R**^{2} → **R**^{2}

Answer The composition `TS` is `Rotation by -90 degrees`: **R**^{2} → **R**^{2}

3) **T** = `Reflection in origin`: **R**^{2} → **R**^{2}

**S** = `Rotation by 90 degrees`: **R**^{2} → **R**^{2}

Answer The composition `TS` is `Rotation by -90 degrees`: **R**^{2} → **R**^{2}

4)
**T** = `Reflection in x-axis`: **R**^{2} → **R**^{2}

**S** = `Embedding as diagonal`: **R** → **R**^{2}

Answer The composition `TS` is `Embedding as skew-diagonal`: **R**^{2} → **R**^{2}

5)
**T** = `Embedding as diagonal`: **R** → **R**^{2}

**S** = `Projection onto x-axis`: **R**^{2} → **R**

Answer The composition `TS` is `Vertical intersection with diagonal`: **R**^{2} → **R**^{2}

6)
**T** = `Projection onto x-axis`: **R**^{2} → **R**

**S** = `Embedding as diagonal`: **R** → **R**^{2}

Answer The composition `TS` is the identity.