Thank you 2 If the product Th T2 of two linear operators on

Thank you

2. If the product Th T2 of two linear operators on a finite dimensional vector s V is invertible, then both T1 and T2 are invertible.

Solution

Let, X and Y be matrices respecitvely of T1 and T2

Then matrix for T1T2 is XY

T1T2 is invertible hence, matrix XY is invertible

det(XY) is non zero

BUt, det(XY)=det(X)det(Y) is non zero

Hence, det(X) and det(Y) is non zero

So, X and Y are invertible

ANd hence, T1 and T2 are invertible