Systems, Matrices, and Determinants · Challenge problem

A $2\times2$ system has coefficient matrix $A$ with $\det A=5$. A new system is formed by replacing the first equation with (three times the first equation) plus (two times the second equation), leaving the second equation unchanged. Find the determinant of the new coefficient matrix. (The answer does not depend on which particular $A$ you started with — only on $\det A$.)