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League of Legend Download Mac - Decision Point

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Case 1:** \( b = 0 \) and \( c = 0 \)

📌 Then, \( a^2 = 1 \) and \( d^2 = 1 \). So, \( a = \pm 1 \) and \( d = \pm 1 \). The diagonal matrices \( egin{pmatrix} \pm 1 & 0 \ 0 & \pm 1 \end{pmatrix} \) satisfy \( T^2 = I \).

📌 Case 2:** \( a + d = 0 \)

📌 Let \( d = -a \). Substituting into equations 1 and 4:

📌 \( bc + a^2 = 1 \)

📌 Both equations are identical. So, \( a^2 + bc = 1 \) holds. Thus, the conditions are \( d = -a \) and \( a^2 + bc = 1 \).

📌 The valid matrices \( T \) are:

📌 T = egin{pmatrix} a & b \ c & -a \end{pmatrix} \quad ext{with} \quad a^2 + bc = 1

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