2. Let
I =
?
?
1 0 0
0 1 0
0 0 1
?
? , A =
?
?
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
?
? , and B = I ? A (a) Calculate AA and BB.
(b) Determine the rank of A.
(c) Determine the rank of B.
(d) Are matrices A and B idempotent?

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