Prove: If A is nonsingular matrix and c is in set of....

buckaroobill

New member
Joined
Dec 16, 2006
Messages
40
This proof was confusing me so if anyone could show me how it is done, then i would appreciate it!

If A is a nonsingular matrix and c is in the set of real numbers w/ c not equal to 0, prove that the inverse of cA (meaning (cA)^-1) is equal to the inverse of A * (1/c).

This is what I have for an answer, but I don't know if it's right.

First, (cA)^-1 = (1/c)A^-1

Then, I said that (cA)^-1 is equal to c^-1 * A^-1 by a theorem.

Therefore, we have c^-1 * A^-1 = (1/c)A^-1

Since there is an A^-1 on both sides, that cancels out, leaving c^-1 = (1/c).

Therefore, (cA)^-1 = (1/c)A^-1.
 
Duplicate post deleted. Please post any further follow-ups to this thread.

Thank you.

Eliz.
 
Top