Let p be an odd prime number and Tp, be the following set of 2×2 matrices Tp={A=[acba]:a,b,c∈{0,1,2,………p−1}} The number of A in Tp, such that A is either symmetric or skew-symmetric or both, and det (A) divisible by p is

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Let p be an odd prime number and {T}_{{p}}, be the following s

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Let p be an odd prime number and $T_{p}$ , be the following set of $2 \times 2$ matrices $T_{p} = {A = [a c b a] : a, b, c \in {0, 1, 2, \dots\dots\dots p - 1}}$ 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

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Let p be an odd prime number and

T_{p}

, be the following set of

2 \times 2

matrices

T_{p} = {A = [a c b a] : a, b, c \in {0, 1, 2, \dots\dots\dots p - 1}}

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

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Question Text

Let p be an odd prime number and

T_{p}

, be the following set of

2 \times 2

matrices

T_{p} = {A = [a c b a] : a, b, c \in {0, 1, 2, \dots\dots\dots p - 1}}

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