FP1 Invariant Points Help Required

The matrix T maps $[br]\begin{pmatrix} x \\ y \end{pmatrix}$ onto

$[br]\begin{pmatrix} a & c \\ b & d \end{pmatrix} *[br]\begin{pmatrix} x \\ y \end{pmatrix} [br]$

$[br]$

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The matrix T maps $[br]\begin{pmatrix} x \\ y \end{pmatrix}$ onto

$[br]\begin{pmatrix} a & c \\ b & d \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix}[br]$ Hence show that invariant points other than the origin exist if Det(T) = a + d -1. I said that $x = ax + cy$ and $y= bx + dy$ and that therefore a=1, c=0, b=0, d=1. I don't understand how I can find the determinate of T from this.