Let A be an n x n matrix. Are the following statements true or false? ? 1. If 5 = 0 then det(A) = 0. ? 2. For any n x n matrices A, B, det(AB) = det(A) det(B). ? 3. If the null space of A is {0} then det(A) = 0. 4. If A is a 3 × 3 matrix with zero determinant, then one column of A must be a multiple of the other one. ? 5. Let A be any square matrix. det(ATA) ≥ 0 ? 6. The determinant of B is defined for all matrices B ? 7. If A is in REF form then det(A) = 0 or 1. 8. If the rref of A is I then det(A) is 1. 9. If det A = 3 then det(24) = 6. 10. If A is a 2 x 2 matrix with zero determinant, then one column of A must be a multiple of the other one.

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A: Let A and B be matrices of size n x n . Here we need to pick a correct or true statements   Then the…

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Q: Every matrix has its determinant. O True False

A: In this question we asked that every Matrix has a determined or not

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A: Aa per our guidelines, we can answer only first three sub-parts. Kindly repost the rest sub-parts…

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Q: Which of the following is FALSE? A. Det (AB) = Det (A) + Det (B) B. Det (AB) = Det (A) Det (B) T C.…

A: The False statement is  Det(AB)= Det(A) + Det(B)

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Q: Find the inverse of the matrices 7. A = -5 2 5 15 3. - 3

A: as per bartleby guidelines i answered 7 and 8 only

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