Invertible Matrix Theorem - Expii
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Invertible Matrix Theorem - Expii
Learn some different ways to tell if a matrix is invertible. For instance, a square matrix is invertible if and only if its determinant is nonzero. You can also tell by checking if the matrix is equivalent (under row operations) to a diagonal matrix with all diagonal entries nonzero.
May 21, 2018
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4. (9 points) Give examples of A and B such that(a) A B is not invertible although A and B are invertible.(b) A B is invertible although A and B are not invertible(c) All of A, B and A B are invertible.(d) In the last case, show that B^-1 A^-1 is also invertible and find a formula for its inverse.(Hint: Check this out A^-1(A B)B^-1)
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