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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