If A is a square matrix of order 3 such that A(adjA) = then |adjA| =

Engineering

Mathematics

Inverse of a Matrix

Properties of Determinant

Transpose and Adjoint of a Matrix

Question

If A is a square matrix of order 3 such that A(adjA) = $[\begin{array}{lll} 2 0 0 \\ 0 2 0 \\ 0 0 2 \end{array}]$ then |adjA| =

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$A (AdjA) = [\begin{array}{lll} 2 0 0 \\ 0 2 0 \\ 0 0 2 \end{array}] = 2 [\begin{array}{lll} 1 0 0 \\ 0 1 0 \\ 0 0 1 \end{array}] = 2 I$

⇒ |A|I = 2I

⇒ |A| = 2

So, |adjA| = |A|^n–1 [Here order = n = 3]

= (2)^3–1 = 2² = 4

Hence option (B) is correct