Question

If matrix `A=[a_(ij)]_(3xx)`, matrix `B=[b_(ij)]_(3xx3)`, where `a_(ij)+a_(ji)=0` and `b_(ij)-b_(ji)=0 AA i`, `j`, then `A^(4)*B^(3)` is
A. Singular
B. Zero matrix
C. Symmetric
D. Skew-Symmetric matrix

Answer 1

Correct Answer - A
`(a)` Here `a_(ij)+a_(ji)=0impliesA^(T)=-A`
and `b_(ij)-b_(ji)=0impliesB^(T)=B`
and `A,B` are `3xx3` matrices,
Hence `|A|=0`, `implies|A^(4)B^(3)|=0` gtbrgt `impliesA^(4)B^(3)` is singular matrix.