試題詳解

二、 Which of the following statements about the multiplicative inverse of a matrix is/are true?
(A) A matrix A is called invertible if there exists a matrix B such that AB is an identity
matrix.
(B) If a matrix is both diagonalizable and invertible, then so is its multiplicative inverse.
(C) Suppose that matrices A of size n x n and D of size m x m are invertible and that
matrix C is of size m X fi； then the following identity is true

(D) Methods for finding the multiplicative inverse of a matrix include LU factorization,
Gaussian elimination, eigen-decomposition, and Gram-Schmidt process.
(E) None of the above are true.