CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
Question

A square matrix A is said to be orthogonal if AA=AA=In
If A is real skew-symmetric matrix is such that A2+I=0, then

A
A is orthogonal matrix
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
A is orthogonal matrix of odd order
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
A is orthogonal matrix of even order
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
none of these
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is D A is orthogonal matrix of even order
Given A is skew-symmetric matrix and A2+I=O
i.e A=A
I=A2=(A)A=AA
A is orthogonal.
Now, AA=Indet(AA)=1
det(A)detA=1(1)ndet(A)2=1 (det(A)=(1)nA)
A is an orthogonal matrix of even order.
Hence, option C.

flag
Suggest Corrections
thumbs-up
0
mid-banner-image
mid-banner-image
similar_icon
Related Videos
thumbnail
lock
Adjoint and Inverse of a Matrix
MATHEMATICS
Watch in App