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If A ,\ B are two nxxn non-singular matr...

If `A ,\ B` are two `nxxn` non-singular matrices, then `A B` is non-singular (b) `A B` is singular (c) `(A B)^(-1)=A^(-1)B^(-1)` (d) `(A B)^(-1)` does not exist

A

AB is non-singylar

B

AB is singular

C

`(AB)^(-1)=A^(-1)B^(-1)`

D

`(AB)^(-1)` does not exist

Text Solution

Verified by Experts

The correct Answer is:
A
We have,
`abs(AB)=absAabsB ne 0 [:' absA ne 0absB ne 0]`
Therefore, AB isa non-singular matrix.
Consequently,`(AB)^(-1)` exists and `(AB)^(-1)=B^(-1)A^(-1)`.
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