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

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

A
AB is non-singular
B
AB is singular
C
$(A B)^{- 1} = A^{- 1} B^{- 1}$
D
$(A B)^{- 1}$ does not exist

Solution:

We have,

$| A B | = | A | | B | \neq 0$ $[∵ | A | \neq 0, | B | \neq 0]$

Therefore, AB is a non-singular matrix.

Consequently, $(A B)^{- 1}$ exists and $(A B)^{- 1} = B^{- 1} A^{- 1}$

Related content

Test your English Vocabulary

CUET Exam Dates 2024 – Application Form, Fees, Eligibility

CBSE Class 12 IP Answer Key 2024,Informatics Practices Paper Solution For SET 1, 2, 3, 4

CUET UG Cut Off 2024, Category, Universities and Colleges Wise Expected Cut Off

Modal Verbs

Helping Verbs

Letter To Your Friend About Your School Trip

Action Verbs

CUET 2024 – List of Colleges and Participating Universities Accepting CUET Exam Score

SRMJEEE Online Test Series – Practice Papers