1. A square matrix A, of order 3, has |A|=5, find |A adj. A|.

let A be a square matrix of order n.
A(adjA)=|A|In , where In be the identity matrix of order n.
therefore
A(adjA)=|A|In=AnIn=An  [|In| =1]
given |A| = 5 and n = 3
therefore
A(adjA)=53=125
hope this helps you.

  • 8

|A adj A| = |A| n-1 here n(order) = 3 therefore |A adj .A| = 5 3-1 = 52 = 25. Hope it helps.

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