# Math Help - Indicate how A^-1 exists

1. ## Indicate how A^-1 exists

Any help is appreciated!

2. You can use determinants to prove it. You know if det(A) = 0, an inverse does NOT exist. So if you take det() of each side:

det(2AB - 3AC) = det(I)

det(A)*(det(2B - 3C)) = 1

Can only be true if det(A) is nonzero, so the inverse must exist.

Oh, and to get the second part, multiply both sides by A inverse.

3. You are given that 2AB+ 3AC= I. Write that as A(2B+ 3C)= I. Now, what is the definition of "inverse"?