# Matrix or Football?

Algebra Level 4

A matrix $H=[h_{jk}]$ is used to keep track of three football players (numbered 1,2 and 3) in three matches (1st,2nd and 3rd).

$Re(h_{jk})=A$ A= number of matches in which both jth and kth players played or both did not play.

If j=k,A=3

$Img(h_{jk})=B$

B = (number of matcher played by kth player) - (number of matches played by jth player)

Let$P=[P_{jk}]$ $P_{jk}=C$ C=1 if jth player played in kth match and C=i otherwise $i=(-1)^{0.5}$

$det(H)=D$ $\left| D\right|=E$

Only in the answer two parallel lines represent det and not absolute value.

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