`Answer:`
\(A=1.\left(-2\right).3.\left(-4\right).5.\left(-6\right).7.\left(-8\right).9.\left(-10\right)\)
\(=-\left(2.3.4.5.6.7.8.9.10\right)\)
\(=-2[\left(2.3.4\right).\left(5.8.9\right).\left(6.7.10\right)]\)
\(=-\left(24.360.420\right)\)
\(=-3628800\)