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Question

Let A be a square matrix of order two such that AAAT=I2. If trace (A)R and entries are complex numbers, number of such matrices possible are

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Solution

Let A=[abcd][a2+b2ac+bdac+bdc2+d2]=[1001]
ac+bd=b=c(a+d)b=0b=0
a2a+1=0,d2d+1=0
a=w,w2,d=w,w2
So two matrices possible.
[w00w],[w200w2]

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