Question

If A = [a_ij] is a 3 × 3 diagonal matrix such that a₁₁ = 1, a₂₂ = 2 and a₃₃ = 3, then find |A|.

Answer 1

Since A is a diagonal matrix, therefore, all it’s non-diagonal members are 0. And a₁₁ = 1, a₂₂ = 2 and a₃₃ = 3

Expanding along R₁

|A| = 1(2 × 3 - 0) = 6