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LatA = [a(ij)](3xx 3). If tr is arithmet...

Lat`A = [a_(ij)]_(3xx 3).` If tr is arithmetic mean of elements of rth row
and `a_(ij )+ a_( jk) + a_(ki)=0` holde for all `1 le i, j, k le 3.`
Matrix A is

A

`A` is a non singular matrix

B

`A` is a singular matrix

C

`sum_(1 let i, j le 3)a_(ij)` is equal to zero

D

`A` is a symmetric matrix

Text Solution

Verified by Experts

The correct Answer is:
B, C
Put `i=j=k`
`a_(ij)=0` and put `k=iimpliesa_(ij)=-a_(ji)`
So, matrix is skew symmetric of odd order.
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