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.
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.
