Why Does exp(A+B) Not Equal exp(A)exp(B) for Certain Matrices?

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Can you please provide an example of 2x2 matrices A and B, where exp(A+B)\neqexp(A).exp(B)
 
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If A and B commute (i.e. AB=BA), then exp(A+B)=exp(A)exp(B). Can you find an example of two 2x2 matrices that don't commute?
 

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