Can someone explain me this Gaussian Method

Question

Hello here is my problem:

Can someone just explain me how did he get that inside that circle. I know everything before that just dont know what did he multiply second row with and added to third row in order to get that. If someone can explain me please. And tell me what I need to study more in order to know how to get that stuff in circled area. Sorry and thanks!

Answer 1

The second row was multiplied by $(1+m)$. Then the corresponding elements were substracted from the elements of the third row.

second column:

$1-m^2-(1+m)(1-m)=1-m^2-(1-m^2)=0$

third column:

$(1-m)-(1+m)(m-1)=1-m-m+1-m^2+m=-m^2-m+2$

Answer 2

Ask yourself: with what do you need to multiply $(1-m)$ to get $1-m^2$ (which is what you want to remove)?

Hint: $1-m^2=1^2-m^2$