Question

If \[A = \left[ a_{ij} \right]\]   is a 3 × 3 diagonal matrix such that a₁₁ = 1, a₂₂ = 2 a₃₃ = 3, then find |A|.

 

Answer 1

\[I\text{ If }A = \left[ a_{ij} \right]\text{ is a diagonal matrix of order n, then }\left| A \right| = a_{11} \times a_{22} \times a_{33} \times . . . \times a_{nn} . \] 
\[\text{ Given }: a_{11} = 1, a_{22} = 2\text{ and }a_{33} = 3\] 
\[ \Rightarrow \left| A \right| = 1 \times 2 \times 3 = 6 \left[\text{ Applying the above property }\right]\]