DeterminantHard

Question

If A, B are two n × n non-singular matrices, then

Options

A.AB is non-singular
B.AB is singular
C.(AB)-1 = A-1 B-1
D.(AB)-1 does not exist

Solution

|A| ≠ 0 and  |B| ≠ 0  ⇒  |AB| ≠ 0
∴ AB is non singular.

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