The value of |B| is equal to

Engineering

Mathematics

Introduction to Determinants

Question

|A|

|A| / 2

2|A|

none of these

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$A = [\begin{array}{lll} a_{11} a_{12} a_{13} \\ a_{21} a_{22} a_{23} \\ a_{31} a_{32} a_{33} \end{array}]$

$B = [\begin{array}{lll} a_{12} + a_{13} a_{11} + a_{13} a_{11} + a_{12} \\ a_{22} + a_{23} a_{21} + a_{23} a_{21} + a_{22} \\ a_{32} + a_{33} a_{31} + a_{33} a_{31} + a_{32} \end{array}]$

X = A + B

$= \frac{1}{| A |} [\begin{array}{lll} c_{11} c_{21} c_{31} \\ c_{12} c_{22} c_{32} \\ c_{13} c_{23} c_{33} \end{array}]$

$= \frac{1}{| A |} [\begin{array}{ccc} 0 & | A | & | A | \\ | A | & 0 & | A | \\ | A | & | A | & 0 \end{array}] \Rightarrow [\begin{array}{lll} 0 1 1 \\ 1 0 1 \\ 1 1 0 \end{array}]$

|A^–1B| = 2

|A^–1| |B| = 2

|B| = 2 |A|

∴ C option is correct

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