if A is a square matrix of order 3, such that / adj.A / = 64 . then find / A' / .

*ans is +8 or -8*

*It can be explained as shown*

*We have*

*A(adj.A) = (adj.A) = |A| ** **I**

* ***| A(adj.A) | = | |A| * I |**

**|A| |adj.A | = |A| | I | ..... ( since | kA | = k ^{n}|A| )**

**|A| |adj.A | = |A| ^{n} * 1**

**| adj.A | = |A| ^{n} / |A|**

**This gives**

**| adj.A | = |A| ^{n-1}**

**where n is the order of the matrix.**

**So in this question **

**| adj.A | = |A| ^{n-1}**

**64 = | A | ^{2}**

**|A| = +8 or -8**

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