# Write the inverse of A in terms of the matrix A

• April 14th 2010, 03:56 PM
DarK
Write the inverse of A in terms of the matrix A
I have no idea where to begin, if someone could help me get started.

Also, I'm a little unsure about what to do for the first question as well (part a).
• April 14th 2010, 04:04 PM
dwsmith
Matrix multiplication general isn't commutative.

$(A-B)(A+B)=A^2+AB-BA-B^2$

If $AB \neq BA$, then $AB-BA$ isn't guaranteed to equal to 0.
• April 15th 2010, 06:00 AM
HallsofIvy
You titled this "write the inverse of A in terms of the matrix A" but then didn't ask about (b)!

If $A^2+ A- I_n= 0$ then $A(A+ I_n)= (A+ I_n)A= I_n$.