wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Let A be a square matrix all of whose entries are integers. Then, which one of the following is true ?

A
lf detA=±1, then A1 exists and all its entries are integers
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
lf detA=±1, then A1 need not exist
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
lf detA=±1, , then A1 exists but all its entries are not necessarily integers
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
lf detA±1, then A1 exists and all its entries are non-integers
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A lf detA=±1, then A1 exists and all its entries are integers
Since A has all integer elements, its cofactors will also be integers. So Adj(A) will have integer elements
So if |A|=±1
we have A1=1|A|Adj(A)=±1×Adj(A)
And hence A1 exists, and has all the elements as integers.

flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Adjoint and Inverse of a Matrix
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon