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Question
Which of the following is an orthogonal matrix
Which of the following is an orthogonal matrix
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Solution
The correct option is B ⎡⎢⎣6/72/73/72/7−3/76/73/76/7−2/7⎤⎥⎦
For A=⎡⎢⎣6/72/7−3/72/73/76/73/7−6/72/7⎤⎥⎦
AT=⎡⎢⎣6/72/73/72/73/7−6/7−3/76/72/7⎤⎥⎦
Thus
AAT=⎡⎢⎣6/72/7−3/72/73/76/73/7−6/72/7⎤⎥⎦⎡⎢⎣6/72/73/72/73/7−6/7−3/76/72/7⎤⎥⎦=⎡⎢⎣100010001⎤⎥⎦=I
Hence A is orthogonal matrix
For A=⎡⎢⎣6/72/7−3/72/73/76/73/7−6/72/7⎤⎥⎦
AT=⎡⎢⎣6/72/73/72/73/7−6/7−3/76/72/7⎤⎥⎦
Thus
AAT=⎡⎢⎣6/72/7−3/72/73/76/73/7−6/72/7⎤⎥⎦⎡⎢⎣6/72/73/72/73/7−6/7−3/76/72/7⎤⎥⎦=⎡⎢⎣100010001⎤⎥⎦=I
Hence A is orthogonal matrix
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