If , find A2.

Engineering

Mathematics

Algebra of Matrices

Multiplication of Matrices

compound angle Formulae

Question

If $A = [\begin{array}{cc} \cos 2 θ & \sin 2 θ \\ - \sin 2 θ & \cos 2 θ \end{array}]$ , find A².

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A = [\begin{array}{cc} \cos 2 θ & \sin 2 θ \\ - \sin 2 θ & \cos 2 θ \end{array}]

A^{2} = [\begin{array}{cc} \cos 2 θ & \sin 2 θ \\ - \sin 2 θ & \cos 2 θ \end{array}] [\begin{array}{cc} \cos 2 θ & \sin 2 θ \\ - \sin 2 θ & \cos 2 θ \end{array}]

A^{2} = [\begin{array}{cc} \cos^{2} 2 θ + \sin^{2} 2 θ & - \cos 2 θsin 2 θ + \cos 2 θsin 2 θ \\ - \sin 2 θcos 2 θ + \sin 2 θcos 2 θ & \sin^{2} 2 θ + \cos^{2} 2 θ \end{array}]

A^{2} = [\begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array}]