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

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

1. A

AB is non-singular

2. B

AB is singular

3. C

$\left(AB{\right)}^{-1}={A}^{-1}{B}^{-1}$

4. D

$\left(AB{\right)}^{-1}$ does not exist

Register to Get Free Mock Test and Study Material

+91

Verify OTP Code (required)

### Solution:

We have,

$|AB|=|A||B|\ne 0$             $\left[\because |A|\ne 0,|B|\ne 0\right]$

Therefore, AB is a non-singular matrix.

Consequently, $\left(AB{\right)}^{-1}$ exists and

Register to Get Free Mock Test and Study Material

+91

Verify OTP Code (required)