1.Let B an nxn matrix such that B^4=0
Show that A=I-B is invertible and A^-1 = I+B+B^2+B^3?
2 Let A an nxn Matrix
a.If A^2=0 show that A is not Invertible
b. If A^2= A and A is not the identity, show that A is not Invertible.
plz help.. i couldnt seem to figure it out?
The definition ofOriginally Posted by firebio
is that
and
(I+ B+ B^2+ B^3)= I(I+ B+ B^2+ B^3)- B(I+ B+ B^2+ B^3))
since
.
(I- B)= (I+ B+ B^2+ B^3)I- (I+ B+ B^2+ B^3)B)
.
a) (proof by contradiction) Suppose A were invertible. Then, multiplying both sides by2 Let A an nxn Matrix
a.If A^2=0 show that A is not Invertible
b. If A^2= A and A is not the identity, show that A is not Invertible.
plz help.. i couldnt seem to figure it out?which is a contradiction because 0 is not invertible.
Do exactly the same thing for b.
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