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Question

Let A=[1121], B=[x1y1], if (A+B)2=A2+B2, find (x,y) is equal to

A
(4,1)
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B
(1,4)
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C
(4,1)
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D
(1,4)
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Solution

The correct option is B (1,4)
(A+B)2=A2+B2+AB+BA=A2+B2

AB=BA

[1121][x1y1]=[x1y1][1121]

[xy22xy3]=[x2x+12yy1]

Comparing, we get

x+1=2,y1=3

x=1,y=4

(x,y)=(1,4)

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