$\displaystyle The\ space\ M_{2}R\ of\ all\ 2x2\ matrices\ over\ R\ can\ be\ identified\ with\ R^4: \left(\begin{array}{cc}A_{11}&A_{12}\\A_{21}&A_{22 }\end{array}\right)\rightarrow\left(\begin{array}{ cc}A_{11}\\A_{12}\\A_{21}\\A_{22}\end{array}\right ) Therefore\ we\ can\ introduce\ on\ M_{2}R\ the\ Euclidean\ metric:\parallel\left(\begin{array}{cc}A_{11}&A_{1 2}\\A_{21}&A_{22}\end{array}\right)\parallel\ =(\mid\ A_{11}-B_{11}\mid^2\ +\mid\ A_{12}-B_{12}\mid^2\ +\mid\ A_{21}-B_{21}\mid^2\ +\mid\ A_{22}-B_{22}\mid^2)^{1/2}\\ in\ particular\ we\ have\ the\ notion\ of\ a\ corresponding\ mapping\ f:\ M_{2}R\rightarrow\ R.\ Clearly\ f\ corresponds\ to\ a\ mapping\ f~\ :\ R^4\rightarrow\ R,\\ f(\left(\begin{array}{cc}A_{11}&A_{12}\\A_{21}&A_{ 22}\end{array}\right))=f~(A_{11}, A_{12},A_{21}, A_{22})\\ Prove\ that\ M_{2}R\rightarrow\ R,a\rightarrow\ det(a)\ is\ continuous$

btw all the large As and Bs should actually be small and the a ---> det(a) should actually be large; A----> det(A). Any help is valued thnx.