試題詳解

2. (5%) Which of the following is true?
(A) A matrix is invertible if and only if its reduced row echelon form is an identity matrix.
(B) For any two n x n matrices A and B, if AB = I_n, then A is invertibie and = B.
(C) If a square matrix has a column consisting of all zeros, then it is not invertible.
(D) If A and B are invertible matrices, then A + B is also invertible.
(E) If A is an n X n matrix such that Ax = b is consistent for every b in Rⁿ, then Ax = b has a unique solution for every b in Rⁿ.