Mark each statement True or False, and justify your answer. a. If A is an n×n matrix such that A² = I, then A is invertible. b. The set W of all nxn matrices A whose trace is equal to 1 is a subspace of M nxn [The trace tr A of the nxn matrix A=(a;;) is defined as the sum of the entries on its main diagonal: tr A = a₁ + a₂2+...+amm ·] 11 nn

Q: Let A be a m×n matrix. Prove that AB and Ba both exist only if B is an n×m matrix.

A: Explanation of the answer is as follows

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A:

Q: Find the null space of the following matrix: A= [( 1,0,2,),(0,1,1),(0,0,0),(0,0,0)]

A:

Q: Let A and B be two square matrices of the same size. Prove that det(AB) = det(BA).

A: Using Determinant and elementary row operations,

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A:

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A: Given:  A=104040158 To find the real canonical form of a given matrix.

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A: See below the explanation

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Q: = 1 -2 2 00 0 -1 0 0 -1

A: Given that A=

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A: Here, CA=I, where I is the identity matrix.

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A: In this question, we have given  A be a 13×19 matrix with rank=11 we need to find the followings:…

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A:

Q: Let A be a 2 × 2 real matrix. Determine conditions on the entries of A so that A2 = I2.

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