Assume all matrices are nx n square matrices. Which of the following statements

Question

Assume all matrices are nx n square matrices. Which of the following statements are true? Choose all that apply Any matrix A can be canceled in AB = AC. If A and B are invertible, then (AB)-AB-1 Of A + B is invertible, thenA +9-1(A + B) = ,n If AB is singular then either A or B is singular. The last row of the reduced row echelon form of a singular matrix contains only zero entry The reduced row echelon form of a singular matrix can contain multiple rows of only zero entry The rows of all zero entry always appear at the end in the reduced row echelon form of a singular matrix. If A and B are invertible, then (AB-BA If A and B are invertible, then (AB AB

Explanation / Answer

1) False, it is true only when A is invertible

2) False, since (AB)-1 = B-1 A-1

3) True, since MM-1 = In where  M is any square invertible matrix of order n.

4) True, a matrix M is said to be singular if det(M)=0. We know that det(AB)=det(A).det(B). Now here det(AB)=0, therefore det(AB)=det(A).det(B)=0, hence either det(A)=0 or det(B)=0. That is either A is singular or B is singular.

5)True

6)True

7)False

8) True

9)False, since (A-1B-1)-1=(B-1)-1(A-1)-1=BA

10) True

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