Originally Posted by

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

H=$\displaystyle \begin{pmatrix}

a & b \\

0 & c

\end{pmatrix}$

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

ive tried

$\displaystyle \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)=$\displaystyle \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.