Is W a subspace of V? If not, state why. Assume that V has the standard operations. (Select all that apply. W is the set of all 2 × 2 matrices of the form 0 b a 0 V = M2,2 O W is a subspace of V. O W is not a subspace of V because it is not closed under addition. OW is not a subspace of V because it is not closed under scalar multiplication.

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A: As per guidelines, we will solve only first three subparts. Kindly repost other subparts separately.

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A: See the solution below.

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A: Using Determinant and elementary row operations,

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A:

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A:

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Q: Suppose that the square matrix A is invertible. Show that the inverse of A is unique.

A: See below the explanation

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A: We have to do both the matrix multiplication.

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A: The transpose of matrix A is,

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A:

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A: Let (a,b,c) be any element of R3, then (a,b,c)=(x,y,0)+(0,y,z)=(x,2y,z) ⇒a=x, b=2y, c=z ⇒a,b,c∈R ⇒…

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A:

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