Practicing Success
If $A=\begin{bmatrix}\cos θ&\sin θ&0\\-\sin θ&\cos θ&0\\0&0&1\end{bmatrix}$ and B is a square matrix of order 3, then $|AB|$ is equal to: |
$|B|^2$ $|B|$ $\sin^2θ|B|$ $\cos^2θ|B|$ |
$|B|$ |
$A=\begin{bmatrix}\cos θ&\sin θ&0\\-\sin θ&\cos θ&0\\0&0&1\end{bmatrix}$ $|AB|=|A||B|$ so |A| → expansion along Row 3 we get $1×\begin{vmatrix}\cos θ&\sin θ\\-\sin θ&\cos θ\end{vmatrix}=\cos^2 θ+\sin^2 θ=1(|A|)$ so $|AB|=|A||B|$ $=|B|$ |