, then Adj(A)

Engineering

Mathematics

Introduction to Determinants

Question

$A = [\begin{array}{ccc} 3 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 3 \end{array}]$ , then Adj(A)

9A^T

2A^T

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We have, $A = [\begin{array}{ccc} 3 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 3 \end{array}]$
co-factor matrix of A is,
$B = [\begin{array}{ccc} 9 & 0 & 0 \\ 0 & 9 & 0 \\ 0 & 0 & 9 \end{array}]$
Thus
$∴ Adj (A) = B^{T} = [\begin{array}{ccc} 9 & 0 & 0 \\ 0 & 9 & 0 \\ 0 & 0 & 9 \end{array}] = 3 [\begin{array}{ccc} 3 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 3 \end{array}] = 3 A$

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