Tentukanlah nilai x dan y yang memenuhi syarat berikut ini ! a) G = [tex]\left[\begin{array}{ccc}y&1\\0&x\end{array}\right][/tex] dan G² = I b) Y = [tex]\lef

[tex] G^{2}=I \\ \left[\begin{array}{ccc}y&1\\0&x\end{array}\right] .\left[\begin{array}{ccc}y&1\\0&x\end{array}\right]=\left[\begin{array}{ccc}1&0\\0&1\end{array}\right] \\ \left[\begin{array}{ccc}y^2&x+y\\0&x^2\end{array}\right]=\left[\begin{array}{ccc}1&0\\0&1\end{array}\right] \\ y^2=1 <=>y=1 atau y=-1 \\ x^2=1 <=>x=1 atau x=-1 \\ \\[/tex]
[tex] F^2=x.F+y.I \\ \left[\begin{array}{ccc}-3&1\\-2&5\end{array}\right].\left[\begin{array}{ccc}-3&1\\-2&5\end{array}\right] = x \left[\begin{array}{ccc}-3&1\\-2&5\end{array}\right]+y \left[\begin{array}{ccc}1&0\\0&1\end{array}\right] \\ \left[\begin{array}{ccc}7&2\\-4&23\end{array}\right]=\left[\begin{array}{ccc}-3x&x\\-2x&5x\end{array}\right]+ \left[\begin{array}{ccc}y&0\\0&y\end{array}\right] \\\left[\begin{array}{ccc}7&2\\-4&23\end{array}\right]=\left[\begin{array}{ccc}-3x+y&x\\-2x&5x+y\end{array}\right][/tex]
[tex]x=2 \\ -3x+y=7 \\ -3.2+y=7 \\ -6+y=7 \\ y=7+6 \\ y=13[/tex]

Ini jawabannya , maaf agak lama ya ...