If I-AB is invertible, then I-BA is invertible. Where I is the identity matrix, and A is m by n, B is n by m.

Let A be an m×n matrix, then ( ). A: AAT =ATA. B: if rank(A) = m, then AT A is invertible. C: if rank(A) = n, then AAT is invertible. D: if rank(A) = n, then AT A is invertible.

Let A be a n×n matrix, then ( ) A: AAT =ATA. B: det(AAT ) = det(AT A). C: if det(A) = 0, then A is invertible. D: if det(A) = 0, then AT is invertible.

Ais an[img=44x19]1803b6a4c8dddc0.png[/img]matrix. A is not invertible if and only if 0 is an eigenvalue of A.

Let A be a 4 by 3 matrix, and r(A)=2, and B is an invertible matrix, then r(AB)=______

Let A be a n×n matrix, then ( ) A: [img=94x23]180348ef1e7493d.png[/img] B: [img=171x28]180348ef2664920.png[/img] C: If [img=85x25]180348ef2f7cdbe.png[/img], then [img=14x19]180348ef37b5dfe.png[/img] is invertible. D: If [img=85x25]180348ef2f7cdbe.png[/img], then [img=22x23]180348ef47fab11.png[/img]is invertible.

The matrix A is[img=44x19]1803b6ad8347a80.png[/img]. If the eqaution Ax=0 has only the trivial solution , thenA is invertible.