The element ai j of square matrix is given by ai j=(i+j) (i-j), then matrix A must be

Question

The element ai j of square matrix is given by ai j=(i+j) (i-j), then matrix A must be (A) Skew-symmetric matrix (B) Triangular matrix (C) Symmetric matrix (D) Null matrix

Tardigrade Admin · Accepted Answer

We have aj i=(j+i)(j-i)=-(i+j)(i-j)=-ai j Hence, matrix is skew-symmetric.

Q. The element $a_{ij}$ of square matrix is given by $a_{ij} = (i + j)$ $(i - j),$ then matrix $A$ must be

Skew-symmetric matrix

Triangular matrix

Symmetric matrix

Null matrix

We have $a_{ji} = (j + i) (j - i) = - (i + j) (i - j) = - a_{ij}$
Hence, matrix is skew-symmetric.

Q. The element aij​ of square matrix is given by aij​=(i+j) (i−j), then matrix A must be