Question

If f(a) = $\begin{bmatrix} \cos\alpha & \sin\alpha \

• \sin\alpha & \cos\alpha \end{bmatrix}$ and a, b, g are angles of triangle

then f(a). f(b).f (g) =

• A. I₂
• B. – I₂
• C. 0
• D. None

Answer 1

Answer: (B)

– I₂

Answer 2

Here f (a) . f (b) . f(g) =$\begin{bmatrix} \cos(\alpha + \beta + \gamma) & \sin(\alpha + \beta + \gamma) \

• \sin(\alpha + \beta + \gamma) & \cos(\alpha + \beta + \gamma) \end{bmatrix}$

= $\begin{bmatrix} \cos\pi & \sin\pi \

• \sin\pi & \cos\pi \end{bmatrix}$=$\begin{bmatrix}
• 1 & 0 \ 0 & - 1 \end{bmatrix}$ = –I₂