# Thread: Centre of a Subgroup

1. ## Centre of a 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.

2. Originally Posted by kashk

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.
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?