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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Q: 5. Consider the following four matrices: ab c ba 2a 2b 2c a-3c b+Sa A= d e f #ME B-f d de f D d-3f…

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