# Thread: Centre of a Subgroup

1. ## Centre of a Subgroup

can someone please help me trying to find the centre of the following subgroup

H= $\begin{pmatrix}
a & b \\
0 & c
\end{pmatrix}$

where a,b,c belong to Reals and ac not equal to zero

ive tried

$\begin{pmatrix}
a & b \\
0 & c
\end{pmatrix}
\begin{pmatrix}
f & g \\
0 & h
\end{pmatrix}
=
\begin{pmatrix}
f & g \\
0 & h
\end{pmatrix}
\begin{pmatrix}
a & b \\
0 & c
\end{pmatrix}$

then equating to find the values of a b and c. but have had no luck

also tried replacing f,g,h with 1's and 0's with no luck

the answer is Z(H)= $\begin{pmatrix}
a & 0 \\
0 & a
\end{pmatrix}$

Got an exam in a couple of days so any help appreciated. Can never do these kinds of questions so a general method would be nice.

2. Originally Posted by kashk
can someone please help me trying to find the centre of the following subgroup

H= $\begin{pmatrix}
a & b \\
0 & c
\end{pmatrix}$

where a,b,c belong to Reals and ac not equal to zero

ive tried

$\begin{pmatrix}
a & b \\
0 & c
\end{pmatrix}
\begin{pmatrix}
f & g \\
0 & h
\end{pmatrix}
=
\begin{pmatrix}
f & g \\
0 & h
\end{pmatrix}
\begin{pmatrix}
a & b \\
0 & c
\end{pmatrix}$

then equating to find the values of a b and c. but have had no luck

also tried replacing f,g,h with 1's and 0's with no luck

the answer is Z(H)= $\begin{pmatrix}
a & 0 \\
0 & a
\end{pmatrix}$

Got an exam in a couple of days so any help appreciated. Can never do these kinds of questions so a general method would be nice.
Go here.

3. in the exam we are supposed to do it by reducing the matrix by comparing the coefficients. Is there a way to do this?