I f m a t r i x A = [ a i j ] 3 × 3 , m a t r i x B = [ b i j ] 3 × 3 w h e r e a i j + a j i = 0 a n d b i j − b j i = 0 , t h e n A 4 . B 3 i s Options: A . &nbspskew-symmetric matrix B . &nbspsingular C . &nbspsymmetric D . &nbspzero matrix

If matrix A=[aij]3×3,matrix B=[bij]3×3 where

Question

I f m a t r i x A = [a_{i j}]_{3 \times 3}, m a t r i x B = [b_{i j}]_{3 \times 3} w h e r e a_{i j} + a_{j i} = 0 a n d b_{i j} - b_{j i} = 0, t h e n A^{4} . B^{3} i s

Options:

A . skew-symmetric matrix

B . singular

C . symmetric

D . zero matrix

Answer: Option B
:
B
Since matrix A is skew-symmetric,

∴ | A | = 0

∴ | A^{4} . B^{3} | = 0

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