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I have been trying to solve a couple of true / false questions, and I am not sure my answers are correct, I would appreciate it if you could verify it.

**The first question is:**

A and B are matrices such that it is possible to calculate:

\[C=AB+B^{t}A^{t}\]

a. A and B are of the same order

b. C is symmetric

c. BA can be calculated

d. A and B are squared matrices

e. \[ABA^{t}\] can be calculated

My answers are: a - false, b - true , c - true, d - false e - false

**The second question is:**

A is a 3x3 not invertible matrix:

a. The system Ax=b has a unique solution for every vector b

b. The system Ax=b has infinite number of solutions for every vector b

c. The matrix kA is not invertible for every real number k.

d. If rank(A)=1, then A has at least one row of 0's.

e. There exist a vector b such that Ax=b has infinite number of solutions.

My answers are: a - false, b - false, c - true, d - true, e - true

Is there something wrong with my solutions ?

Thanks a million !