Some Magic Square
\begin{align*} 3\begin{pmatrix} 2 & 0 & 1 \\ 0 & 1 & 2 \\ 1 & 2 & 0 \\ \end{pmatrix} +\begin{pmatrix} 2 & 0 & 1 \\ 0 & 1 & 2 \\ 1 & 2 & 0 \\ \end{pmatrix}^m = \begin{pmatrix} 6 & 0 & 3 \\ 0 & 3 & 6 \\ 3 & 6 & 0 \\ \end{pmatrix} +\begin{pmatrix} 1 & 0 & 2 \\ 2 & 1 & 0 \\ 0 & 2 & 1 \\ \end{pmatrix} = \begin{pmatrix} 7 & 0 & 5 \\ 2 & 4 & 6 \\ 3 & 8 & 1 \\ \end{pmatrix} \equiv \begin{pmatrix} 8 & 1 & 6 \\ 3 & 5 & 7 \\ 4 & 9 & 2 \\ \end{pmatrix} \end{align*}
\begin{align*} 4\begin{pmatrix} 0 & 1 & 2 & 3 \\ 3 & 2 & 1 & 0 \\ 1 & 0 & 3 & 2 \\ 2 & 3 & 0 & 1 \\ \end{pmatrix} +\begin{pmatrix} 0 & 1 & 2 & 3 \\ 3 & 2 & 1 & 0 \\ 1 & 0 & 3 & 2 \\ 2 & 3 & 0 & 1 \\ \end{pmatrix}^t = \begin{pmatrix} 0 & 4 & 8 & 12 \\ 12 & 8 & 4 & 0 \\ 4 & 0 & 12 & 8 \\ 8 & 12 & 10 & 4 \\ \end{pmatrix} +\begin{pmatrix} 0 & 3 & 1 & 2 \\ 1 & 2 & 0 & 3 \\ 2 & 1 & 3 & 0 \\ 3 & 0 & 2 & 1 \\ \end{pmatrix} = \begin{pmatrix} 0 & 7 & 9 & 14 \\ 13 & 10 & 4 & 3 \\ 6 & 1 & 15 & 8 \\ 11 & 12 & 2 & 5 \\ \end{pmatrix} \equiv \begin{pmatrix} 1 & 8 & 10 & 15 \\ 14 & 11 & 5 & 4 \\ 7 & 2 & 16 & 9 \\ 12 & 13 & 3 & 6 \\ \end{pmatrix} \end{align*}
\begin{align*} 4\begin{pmatrix} 1 & 2 & 3 & 0 \\ 0 & 3 & 2 & 1 \\ 2 & 1 & 0 & 3 \\ 3 & 0 & 1 & 2 \\ \end{pmatrix} +\begin{pmatrix} 1 & 2 & 3 & 0 \\ 0 & 3 & 2 & 1 \\ 2 & 1 & 0 & 3 \\ 3 & 0 & 1 & 2 \\ \end{pmatrix}^t \equiv \begin{pmatrix} 6 & 9 & 15 & 4 \\ 3 & 16 & 10 & 5 \\ 12 & 7 & 1 & 14 \\ 13 & 2 & 8 & 11 \\ \end{pmatrix} \end{align*}
\begin{align*} 4\begin{pmatrix} 3 & 0 & 1 & 2 \\ 2 & 1 & 0 & 3 \\ 0 & 3 & 2 & 1 \\ 1 & 2 & 3 & 0 \\ \end{pmatrix} +\begin{pmatrix} 3 & 0 & 1 & 2 \\ 2 & 1 & 0 & 3 \\ 0 & 3 & 2 & 1 \\ 1 & 2 & 3 & 0 \\ \end{pmatrix}^t \equiv \begin{pmatrix} 16 & 3 & 5 & 10 \\ 9 & 6 & 4 & 15 \\ 2 & 13 & 11 & 8 \\ 7 & 12 & 14 & 1 \\ \end{pmatrix} \end{align*}
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\begin{align*} 5\begin{pmatrix} 0 & 1 & 2 & 3 & 4 \\ 2 & 3 & 4 & 0 & 1 \\ 4 & 0 & 1 & 2 & 3 \\ 1 & 2 & 3 & 4 & 0 \\ 3 & 4 & 0 & 1 & 2 \\ \end{pmatrix} +\begin{pmatrix} 0 & 1 & 2 & 3 & 4 \\ 2 & 3 & 4 & 0 & 1 \\ 4 & 0 & 1 & 2 & 3 \\ 1 & 2 & 3 & 4 & 0 \\ 3 & 4 & 0 & 1 & 2 \\ \end{pmatrix}^m = \begin{pmatrix} 0 & 5 & 10 & 15 & 20 \\ 10 & 15 & 20 & 0 & 5 \\ 20 & 0 & 5 & 10 & 15 \\ 5 & 10 & 15 & 20 & 0 \\ 15 & 20 & 0 & 5 & 10 \\ \end{pmatrix} +\begin{pmatrix} 4 & 3 & 2 & 1 & 0 \\ 1 & 0 & 4 & 3 & 2 \\ 3 & 2 & 1 & 0 & 4 \\ 0 & 4 & 3 & 2 & 1 \\ 2 & 1 & 0 & 4 & 3 \\ \end{pmatrix} = \begin{pmatrix} 4 & 8 & 12 & 16 & 20 \\ 11 & 15 & 24 & 3 & 7 \\ 23 & 2 & 6 & 10 & 19 \\ 5 & 14 & 18 & 22 & 1 \\ 17 & 21 & 0 & 9 & 13 \\ \end{pmatrix} \equiv \begin{pmatrix} 5 & 9 & 13 & 17 & 21 \\ 12 & 16 & 25 & 4 & 8 \\ 24 & 3 & 7 & 11 & 20 \\ 6 & 15 & 19 & 23 & 2 \\ 18 & 22 & 1 & 10 & 14 \\ \end{pmatrix} \end{align*}
\begin{align*} 5\begin{pmatrix} 0 & 1 & 2 & 3 & 4 \\ 2 & 3 & 4 & 0 & 1 \\ 4 & 0 & 1 & 2 & 3 \\ 1 & 2 & 3 & 4 & 0 \\ 3 & 4 & 0 & 1 & 2 \\ \end{pmatrix} +\begin{pmatrix} 0 & 1 & 2 & 3 & 4 \\ 2 & 3 & 4 & 0 & 1 \\ 4 & 0 & 1 & 2 & 3 \\ 1 & 2 & 3 & 4 & 0 \\ 3 & 4 & 0 & 1 & 2 \\ \end{pmatrix}^t = \begin{pmatrix} 0 & 5 & 10 & 15 & 20 \\ 10 & 15 & 20 & 0 & 5 \\ 20 & 0 & 5 & 10 & 15 \\ 5 & 10 & 15 & 20 & 0 \\ 15 & 20 & 0 & 5 & 10 \\ \end{pmatrix} +\begin{pmatrix} 0 & 2 & 4 & 1 & 3 \\ 1 & 3 & 0 & 2 & 4 \\ 2 & 4 & 1 & 3 & 0 \\ 3 & 0 & 2 & 4 & 1 \\ 4 & 1 & 3 & 0 & 2 \\ \end{pmatrix} = \begin{pmatrix} 0 & 7 & 14 & 16 & 23 \\ 11 & 18 & 20 & 2 & 9 \\ 22 & 4 & 6 & 13 & 15 \\ 8 & 10 & 17 & 24 & 1 \\ 19 & 21 & 3 & 5 & 7 \\ \end{pmatrix} \equiv \begin{pmatrix} 1 & 8 & 15 & 17 & 24 \\ 12 & 19 & 21 & 3 & 10 \\ 23 & 5 & 7 & 14 & 16 \\ 9 & 11 & 18 & 25 & 2 \\ 20 & 22 & 4 & 6 & 8 \\ \end{pmatrix} \end{align*}
\begin{align*} 5\begin{pmatrix} 4 & 0 & 3 & 1 & 2 \\ 1 & 2 & 0 & 3 & 4 \\ 2 & 3 & 1 & 4 & 0 \\ 3 & 4 & 2 & 0 & 1 \\ 0 & 1 & 4 & 2 & 3 \\ \end{pmatrix} +\begin{pmatrix} 4 & 0 & 3 & 1 & 2 \\ 1 & 2 & 0 & 3 & 4 \\ 2 & 3 & 1 & 4 & 0 \\ 3 & 4 & 2 & 0 & 1 \\ 0 & 1 & 4 & 2 & 3 \\ \end{pmatrix}^m \equiv \begin{pmatrix} 23 & 2 & 19 & 6 & 15 \\ 10 & 14 & 1 & 18 & 22 \\ 11 & 20 & 7 & 24 & 3 \\ 17 & 21 & 13 & 5 & 9 \\ 4 & 8 & 25 & 12 & 16 \\ \end{pmatrix} \end{align*}
\begin{align*} 5\begin{pmatrix} 4 & 0 & 3 & 1 & 2 \\ 1 & 2 & 0 & 3 & 4 \\ 2 & 3 & 1 & 4 & 0 \\ 3 & 4 & 2 & 0 & 1 \\ 0 & 1 & 4 & 2 & 3 \\ \end{pmatrix} +\begin{pmatrix} 4 & 0 & 3 & 1 & 2 \\ 1 & 2 & 0 & 3 & 4 \\ 2 & 3 & 1 & 4 & 0 \\ 3 & 4 & 2 & 0 & 1 \\ 0 & 1 & 4 & 2 & 3 \\ \end{pmatrix}^t \equiv \begin{pmatrix} 25 & 2 & 18 & 9 & 11 \\ 6 & 13 & 4 & 20 & 22 \\ 14 & 16 & 7 & 23 & 5 \\ 17 & 24 & 15 & 1 & 8 \\ 3 & 10 & 21 & 12 & 19 \\ \end{pmatrix} \end{align*}
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\begin{align*} 6\begin{pmatrix} 5 & 5 & 0 & 0 & 0 & 5 \\ 1 & 4 & 4 & 1 & 4 & 1 \\ 3 & 2 & 3 & 3 & 2 & 2 \\ 2 & 3 & 2 & 2 & 3 & 3 \\ 4 & 1 & 1 & 4 & 1 & 4 \\ 0 & 0 & 5 & 5 & 5 & 0 \\ \end{pmatrix} +\begin{pmatrix} 5 & 5 & 0 & 0 & 0 & 5 \\ 1 & 4 & 4 & 1 & 4 & 1 \\ 3 & 2 & 3 & 3 & 2 & 2 \\ 2 & 3 & 2 & 2 & 3 & 3 \\ 4 & 1 & 1 & 4 & 1 & 4 \\ 0 & 0 & 5 & 5 & 5 & 0 \\ \end{pmatrix}^t = \begin{pmatrix} 30 & 30 & 0 & 0 & 0 & 30 \\ 6 & 24 & 24 & 6 & 24 & 6 \\ 18 & 12 & 18 & 18 & 12 & 12 \\ 12 & 18 & 12 & 12 & 18 & 18 \\ 24 & 6 & 6 & 24 & 6 & 24 \\ 0 & 0 & 30 & 30 & 30 & 0 \\ \end{pmatrix} +\begin{pmatrix} 5 & 1 & 3 & 2 & 4 & 0 \\ 5 & 4 & 2 & 3 & 1 & 0 \\ 0 & 4 & 3 & 2 & 1 & 5 \\ 0 & 1 & 3 & 2 & 4 & 5 \\ 0 & 4 & 2 & 3 & 1 & 5 \\ 5 & 1 & 2 & 3 & 4 & 0 \\ \end{pmatrix} = \begin{pmatrix} 35 & 31 & 3 & 2 & 4 & 30 \\ 11 & 28 & 26 & 9 & 25 & 6 \\ 18 & 16 & 21 & 20 & 13 & 17 \\ 12 & 19 & 15 & 14 & 22 & 23 \\ 24 & 10 & 8 & 27 & 7 & 29 \\ 5 & 1 & 32 & 33 & 34 & 0 \\ \end{pmatrix} \equiv \begin{pmatrix} 36 & 32 & 4 & 3 & 5 & 31 \\ 12 & 29 & 27 & 10 & 26 & 7 \\ 19 & 17 & 22 & 21 & 14 & 18 \\ 13 & 20 & 16 & 15 & 23 & 24 \\ 25 & 11 & 9 & 28 & 8 & 30 \\ 6 & 2 & 33 & 34 & 35 & 1 \\ \end{pmatrix} \end{align*}
m:mirrar transform
t:transpose transfrom

The mathmatican Euler seems to have thought a lot about magic square,
But I have no knowlage of them.
How to make magic squares here is my own idea.
If you use this way on the Excel, You can get many magic square.
It is up to the professinal mathematician to investigate in detal. by Yoji Hitomi