a) Show that AB = AB, where A and B are two arbitrary vectors. I want...

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a) Show that AB" = AB, where A and B are two arbitrary vectors. I want you to do it in two ways. First by writing out the full expression explicitly in terms of the vector components. Next, by "formally" manipulating the indices using the metric . Notice that this way is much faster! b) Recall from class that the metric nu can be written in matrix form. Find its inverse (in matrix form) and denote it by na Then show using the appropriate matrix components that n = a, where Sa is the Kronecker delta. This is basically the statement that the two matrices are inverses of each other. c) Show that the inverse metric can be used to raise indices, meaning that Aa = n8 AB Show it by explaining what happens to each component of the A vector. a) Show that AB" = AB, where A and B are two arbitrary vectors. I want you to do it in two ways. First by writing out the full expression explicitly in terms of the vector components. Next, by "formally" manipulating the indices using the metric . Notice that this way is much faster! b) Recall from class that the metric nu can be written in matrix form. Find its inverse (in matrix form) and denote it by na Then show using the appropriate matrix components that n = a, where Sa is the Kronecker delta. This is basically the statement that the two matrices are inverses of each other. c) Show that the inverse metric can be used to raise indices, meaning that Aa = n8 AB Show it by explaining what happens to each component of the A vector.