SOLUTION: Suppose A and B are n × n matrices. If A and B are invertible, then A B is
invertible. Suppose one or both of A and B are singular, what can you say
about the invertibility of A
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invertible. Suppose one or both of A and B are singular, what can you say
about the invertibility of A
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Question 1165295: Suppose A and B are n × n matrices. If A and B are invertible, then A B is
invertible. Suppose one or both of A and B are singular, what can you say
about the invertibility of A B? Explain your reasoning. Answer by Edwin McCravy(20054) (Show Source):
The determinant of a product of square matrices is equal to the product of
their determinants.
The determinant of a square matrix is 0 if and only if the matrix is singular.
Therefore if one or both of A and B is (are) singular, its (their)
determinant(s) is (are) 0, and the product of their determinants is 0, and AB
is singular.
Edwin
