Given A = \( \begin{bmatrix} cosa& sina \\[0.3em] -sina& cosa \\[0.3em] \end{bmatrix}\), We will find A’
\(\Rightarrow\) \(
\begin{bmatrix}
1& 0 \\[0.3em]
0& 1 \\[0.3em]
\end{bmatrix}\) [Using cos2a + sin2a = 1 and commutative law a.b = b.a i.e. sina cosa = cosa sina]
RHS = I \(\Rightarrow\) \(
\begin{bmatrix}
1& 0 \\[0.3em]
0& 1 \\[0.3em]
\end{bmatrix}\)
LHS = RHS
Hence proved.