Write the inverse of A in terms of the matrix A

**DarK** · April 14th 2010, 03:56 PM

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).

**dwsmith** · April 14th 2010, 04:04 PM

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.

**HallsofIvy** · April 15th 2010, 06:00 AM

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 $A(A+ I_n)= (A+ I_n)A= I_n$ .

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