Question

If A = [a_ij] is a 3 × 3 scalar matrix such that a₁₁ = 2, then write the value of |A|.

 

Answer 1

A scalar matrix is a diagonal matrix, in which all the diagonal elements are equal to a given scalar number.
\[\text{ Given: }A = \left[ a_{i j} \right]\text{ is 3} \times\text{ 3 matrix, where }a_{11} = 2 \] 
\[ \Rightarrow A = \begin{bmatrix} 2 & 0 & 0\\0 & 2 & 0\\0 & 0 & 2 \end{bmatrix} \] 
\[ \Rightarrow \left| A \right| = \begin{vmatrix} 2 & 0 & 0\\0 & 2 & 0\\ 0 & 0 & 2 \end{vmatrix}\] 
\[ = 2 \times \begin{vmatrix} 2 & 0\\ 0 & 2 \end{vmatrix} \left[\text{ Expanding along }C_1 \right]\] 
\[ = 2 \times 2 \times 2 = 8\]