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Answer : The LaTeX macros \begin{equation} and \[ both initiate a display-math group, and the macros \end{equation} and \] both terminate a display-math group. (In addition, the equation environment provides a method for numbering the equations, whereas \[ ... \] does not.) The LaTeX macros \begin{equation} and \[ are designed purposefully so as not to let users open a display-math group twice; this is why you're getting the error message "Bad math environment delimiter" when LaTeX encounters \[ after having processed \begin{equation} . The upshot: Use one or the other method for setting up a display-math group, but don't use both simultaneously. For a more-detailed discussion of how various LaTeX displaymath environments are set up, see this answer to the question "What are the differences between $$ , \[ , align , equation and displaymath ?" Shameless self-citation alert! I can't improve @Mico 's correct accepted answer to the qu...

Answer : It is not generally possible to do so. For a concrete example, we know that there can exist no permutation matrices P , Q P,Q P , Q such that P\pmatrix{1&2\\2&1}Q = \pmatrix{2&1\\2&1} If such a P P P and Q Q Q existed, then both matrices would necessarily have the same rank. Let me add one more argument: For n ≥ 2 n \ge 2 n ≥ 2 : Suppose the entries in the n × n n \times n n × n matrix A A A are all distinct. Then there are ( n 2 ) ! (n^2)! ( n 2 )! distinct permutations of A A A . There are n ! n! n ! row-permutations of A A A (generated by premultiplication by various permutation matrices), and n ! n! n ! col-permutations of A A A (generated by post-multiplication by permutation matrices). If we consider all expressions of the form R A C RAC R A C where R R R and C C C each range independently over all n ! n! n ! permutation matrices, we get at most ( n ! ) 2 (n!)^2 ( n ! ) 2 possible results. But for n > 1 n > 1 n > 1...