Question

if A is a square matrix satisfying A'A=I write the value of IAI

Answer 1

$\textbf{Concept:}$

$\text{If A and B are square matrices of same order, then}$

$\boxed{\bf\,|AB|=|A|\,|B|}$

$\textbf{Given:}$

$\text{A is a square matrix with A'A=I}$

$\textbf{To find: |A| }$

$A'A=I$

$\implies|A'A|=|I|$

$\implies|A'|\,|A|=|I|$

$\text{We know that |A'|=|A| }$

$\implies|A|\,|A|=|I|$

$\implies|A|^2=1$

$\implies\boxed{\bf|A|=\pm\,1}$

$\therefore\textbf{The value of |A| is \bf\,\pm\,1 }$

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Answer 2

Answer: ±1

Step-by-step explanation:

Given, A'A=I

Then |A'A|=I

|A'| |A|=|I|

|A| |A|=|I| (since |A'|=|A|)

|A|²=1 (since |I|=1)

|A|=±1 (Ans.)