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.
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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