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If |{:(a+ib,c+id),(-c+id,a-ib):}|xx|{:(a...

If `|{:(a+ib,c+id),(-c+id,a-ib):}|xx|{:(alpha-ibeta,gamma-idelta),(-gamma-idelta,alpha+ibeta):}|=|{:(A-iB,C-iD),(-C-iD,A+iB):}|`, write down the values of A, B, C, `(i=sqrt(-1))`. Hence show that, the product of two sums, each of four squares, can be expressed as the sum of four squares.

Text Solution

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The correct Answer is:
`A=a alpha+b beta-c gamma+d delta, B=a beta-b alpha-balpha+c delta+d gamma`,
` C=a gamma+b delta+calpha-d beta, D=a delta-b gamma-b gamma-c beta-d alpha`,
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