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a) If A is a squared matrix for which

\[A^{2}-A=0\]

then A=0 or A=i

b) If A and B are diagonal matrices, then Ab=BA

c) A 4X4 matrix with eigenvalues 1,0,-1,2 is "diagonlizable"

d) The dimension of the polynomials space of order 3 (ax^3+bx^2+...) is 4

e) If two vectors are linearly dependent, then one is necessarily a multiplication of the other

'a' is correct

'b', not sure, I tried one example, it worked

'c' Each eigenvalue appears once, so it's not possible to have an eigenvalue which appears twice with corresponding 1 eigenvector (for example)

'd' Isn't it 4 ?

'e' I think so....

will appreciate your help