Determine if the following statements are true or false. (a) A square matrix has an inverse if the matrix has a nonzero determinant. (b) The product of a column vector and a row vector is defined. (c) A matrix is said to be singular, if the matrix has an inverse. (d) All identity matrices are diagonal matrices and vice versa. (e) All reduced row echelon matrices are row echelon matrices. (f) Addition of any matrices to a null matrix of the same order is defined and results a null matrix.

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