Let A be a 3 × 3 square matrix, such that A (adj A) = 2I, where I… - Vidyadip

Question

Let A be a 3 × 3 square matrix, such that A (adj A) = 2I, where I is the identity matrix. Write the value of |adj A|.

✓

Answer

$\because$ A(adj (A)) = |A|I
2I = |A|I (Given A(adj A) = 2I)
|A| = 2
Also, |adj A| = |A|^n-1
= (2)^3-1
= (2)²
= 4
|adj A| = 4

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