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Question
Compute the indicated product:
`[(a,b),(-b,a)][(a,-b),(b,a)]`
Solution
`[(a,b),(-b,a)][(a,-b),(b,a)]`
`[(a,b),(-b,a)][(a, -b),(b,a)]`
`=[(a(a) + b(b), a(-b)+ b(a)), (-b(a) + a(b), -b(-b) + a(a))]`
`= [(a^2+b^2, -ab + ab), (-ab+ab, b^2 + a^2)] = [(a^2+b^2, 0),(0, a^2+ b^2)]`
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