1. Let f(z): az + b cz + d and g(z) = 02 +B yz +8 be represented by the matrices a b A-(28) and B-(8) = d respectively. Show that the composition fo g is represented by the matrix AB. Find a formula for the inverse transform f1. Find a Möbius transformation that maps the three points 0, 1, oo onto the three points -1, -i, 1.

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