Question
If A= [ array ccc 0 & c & -b \\ -c & 0 & a \\ b & -a & 0 array ] and B= [ array ccc a^2 & a b & a c \\ a b & b^2 & b c \\ a c & b c & c^2 array ] , then A B is equal to
BITSAT
Mathematics
Matrices
2023
BITSAT 2023 (Memory Based Paper 2)
BITSAT Mathematics Question (2023) — Solution
Options
- A. B
- B. A
- C. O
- D. I
Answer
C. O
Step-by-step solution
aligned & A B= [ array ccc 0 & c & -b \\ -c & 0 & a \\ b & -a & 0 array ] [ array ccc a^2 & a b & a c \\ a b & b^2 & b c \\ a c & b c & c^2 array ] \\ & A B= [ array ccc a b c-a b c & b^2 c-b^2 c & b c^2-b c^2 \\ -a^2 c+a^2 c & -a b c+a b c & -a c+a c \\ a^2 b-a^2 b & a b^2-a b^2 & a b c-a b c array ] \\ & = [ array lll 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 array ]= O \\ & aligned
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