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Permutation

14 Let p be a...

Question

14 Let p be an odd number and T(p) be the following set of 22 matrices ( matrix given below in image Q - the number of A in T(p) such that A is either symmetric or skew symmetric or both ,and det(A) divisible by p is 1) (p-1) 2) 2(p-1) 3) (p-1)+1 4)2p-1

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p

T_{p}

2 \times 2

T_{p} = {A = [\begin{matrix} a & b c & a \end{matrix}] : a, b, c \in {0, 1, \dots ., p - 1}}

T_{p}

A

T_{p}

A

A

p

2 \times 2

A = [a_{j j}] w h e r e a_{j j} ϵ {0, 1, 2, 3, 4}

a_{11} + a_{12} + a_{21} + a_{22} = 4

A

\times

- 1

0

1

0

1

(- 1)

L = ⎡ ⎢ ⎣ \begin{matrix} 2 & 3 & 5 4 & 1 & 2 1 & 2 & 1 \end{matrix} ⎤ ⎥ ⎦ = P + Q,

P

Q

P

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