Label the following statements as true or false. In each part, V, W, and Z denote vector...

Label the following statements as true or false. In each part, V, W, and Z denote vector spaces with ordered (finite) bases α, β, and γ, respectively; T: V → W and U: W → Z denote linear transformations; and A and B denote matrices.(a)

(b) [T(v)]_β = for all v ∈ V.

(c) [U(w)]_β = for all w ∈ W.

(d) [IV]_α = I.

(e)

(f) A ² = I implies that A = I or A = −I.

(g) T = L_A for some matrix A.

(h) A2 = O implies that A = O, where O denotes the zero matrix.

(i) L_A+B = L_A + L_B.

(j) If A is square and A_ij = δ_ij for all i and j, then A = I.