The following item consists of two statements, one labelled the Assertion (A) and the other labelled the Reason (R). You are to examine these two statements carefully and decide if the Assertion (A) and Reason (R) are individually true and if so, whether the reason is a correct explanation of the Assertion. Select your answer using the codes given below :
Assertion (A) : `M=[{:(5,10),(4,8):}]` is invertible.
Reason (R) : M is singular.

Options

A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true but R is not the correct explanation of A
C. A is true but R is false
D. A is false but R is true

Answer

D

Explanation

(A) Consider `M = [{:(5,10),(4,8):}]`
Now, `|M|=|{:(5,10),(4,8):}|=40 - 40 = 0`
Since, |M| = 0
`therefore` M is not in vertible.
(R) Since, determinant of M is zero therefore M is singular matrix.
Therefore, A is false and R is true.