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if a is a square matrix of order 3 such that adj a=64 find (a)

Posted by Arjun Arjun 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

We know that, for a square matrix of order n,
|adj (A) |= |A|^n-1
Here, the order of A is 3{tex}\times {/tex}3 ,therefore n = 3
Now, |adj (A) | =|A|{tex}^{3-1}{/tex} = |A|²
Given, |adj (A)|= 64,

Therefore,64 =|A|²
{tex}\Rightarrow{/tex} (8)² =|A|²
{tex}\Rightarrow{/tex} |A|= ± 8 [taking square root]

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