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Hi,
I was wondering if anyone could help with these questions on matrices i can't get my head around them at all !!
Let A = 1 -2 -2 -2
-2 1 -2 -2
-2 -2 1 -2
-2 -2 -2 1
Show that (3I - A)² is equal to a certain scalar multiple of 3I - A. Hence prove that A is nonsingular and find A-¹.
And
Nonsingular nxn matrices A, B are given to satisfy (A + B)-¹ = A-¹ + B-¹.
Show that C = -C-¹ - I where C = A-¹ B. Deduce that (A-¹ B)³ = I
We have not done the determinant yet so i cant use that i have the answer but i still dont get how to do it. I would be grateful for any advice.
Thanks
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The definition of a singular matrix is one which does not have an inverse. In order to determine wether a matrix has an inverse or not one has to evaluate it's determinant. The definition is simply:
A matrix is singular if and only if its determinant is 0
So given that you say you have not yet covered determinants how would you be expected to determine if a matrix is singular or not?
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