In The South Of E C To The South Of E C Ba E Ab E C A E Aa Ef Bc F E Be E Ba A E F A E

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  • If $A$ and $B$ are $nimes n$ matrices such that $AB = BA$ that is, $A$ and $B$ commute , show that $$ e^{A B}=e^A .

  • In general, AB = BA, even if A and B are both square. If AB = BA, then we say that A and B commute. For a general matrix A, .

  • Proof Let E,E, ,Ek be elementary matrices that correspond to elementary row operations converting A into I. Then .

  • Possibilities either ab = e or ab = c. If we reverse the role of a and b in the previous paragraph, then we nd that there are .

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