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BITSAT 2023Paper 2
Exam
BITSAT
Year
2023
Paper
Paper 2
Subject
Mathematics
Chapter
Matrices

BITSAT 2023 · Paper 2 · Mathematics · Matrices

If A=[ array ccc 0 & c & -b -c & 0 & a b & -a & 0 array ] and B=[...

\\  If \text{ If }A=\left[0c−b−c0ab−a0\begin{array}{ccc}\\ 0 & c & -b \\ \\ -c & 0 & a \\ \\ b & -a & 0 \\ \end{array}\right]  and \text{ and }B=\left[a2abacabb2bcacbcc2\begin{array}{ccc}\\ a² & a b & a c \\ \\ a b & b² & b c \\ \\ a c & b c & c² \\ \end{array}\right] , \text{, }\\ \\ then ABA B is equal to

Options

  1. A
    B
  2. B
    A
  3. C
    O
  4. D
    I

Correct answer

C.
O

Step-by-step solution


AB=[0c−b−c0ab−a0][a2abacabb2bcacbcc2]AB=[abc−abcb2c−b2cbc2−bc2−a2c+a2c−abc+abc−ac+aca2b−a2bab2−ab2abc−abc]=[000000000]=O\begin{aligned} &\quad A B=\left[\begin{array}{ccc}0 & c & -b \\ -c & 0 & a \\ b & -a & 0\end{array}\right]\left[\begin{array}{ccc}a^2 & a b & a c \\ a b & b^2 & b c \\ a c & b c & c^2\end{array}\right] \\ & A B=\left[\begin{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\end{array}\right] \\ & =\left[\begin{array}{lll}0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{array}\right]=\mathrm{O} \\ & \end{aligned}
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