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If A and B are orthogonal matrices of the same order, then prove that AB is also an orthogonal Matrix.

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Detailed Solution

Since A and B re orthogonal matrices. Therefore, AAT=ATA=I and BBT=BTB=Inow,ABABT=ABBTAT =ABBTAT=AIAT =AAT=ISimilarly, we can prove that (AB)T(AB)=I(AB)(AB)T=I=(AB)T(AB) Hence, AB is an orthogonal matrix.

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