Label the following statements as being true or false.(a) An elementary matrix is always square.(b) The only entries of an elementary matrix are zeros and ones.(c) The n x n identity matrix is an elementary matrix. '(d) The product of two n x n elementary matrices is an elementary matrix.(e) The inverse of an elementary matrix is an elementary matrix.(f) The sum of two n x n elementary matrices is an elementary matrix.(g) The transpose of an elementary matrix is an elementary matrix.(h) If B is a matrix that can be obtained by performing an elementary rowoperation on a matrix A, then B can also be obtained by performing anelementary column operation on A.(i) If B is a matrix that can be obtained by performing an elementary rowoperation on a matrix A, then A can be obtained by performing anelementary row operation on B.

Linear Algebra: A Modern Introduction
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Chapter4: Eigenvalues And Eigenvectors
Section4.4: Similarity And Diagonalization
Problem 41EQ: In general, it is difficult to show that two matrices are similar. However, if two similar matrices...
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Label the following statements as being true or false.
(a) An elementary matrix is always square.
(b) The only entries of an elementary matrix are zeros and ones.
(c) The n x n identity matrix is an elementary matrix. '
(d) The product of two n x n elementary matrices is an elementary matrix.
(e) The inverse of an elementary matrix is an elementary matrix.
(f) The sum of two n x n elementary matrices is an elementary matrix.
(g) The transpose of an elementary matrix is an elementary matrix.
(h) If B is a matrix that can be obtained by performing an elementary row
operation on a matrix A, then B can also be obtained by performing an
elementary column operation on A.
(i) If B is a matrix that can be obtained by performing an elementary row
operation on a matrix A, then A can be obtained by performing an
elementary row operation on B.

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