Prove that set $\mathbb{S}$ forms group under matrix multiplication

268 Views Asked by At

I have give the following set to prove that $$\mathbb{S} = \left \{\begin{bmatrix} 1&0 \\ 0&1 \end{bmatrix},\begin{bmatrix} 0&-1\\ 1&-1 \end{bmatrix},\begin{bmatrix} -1&1\\ -1&0 \end{bmatrix} \right \}$$ forms group under matrix multiplication. I already know how to check if the certain set obey the axioms in order to be a group, but following set has finite number of elements(matrices). I was struggling to proceed with this example. Your advice would be appreciate.