If A is a square matrix of order n - n such that - A - then write the value of -A-

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Standard XII

Mathematics

Inverse of a Matrix

If A is a squ...

Question

If A is a square matrix of order n × n such that $| A | = λ$ , then write the value of |−A|.

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Solution

$|A| = λ [Order of A is n] \Rightarrow |- A| = {(- 1)}^{n} |A| = {(- 1)}^{n} λ$

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If A is a square matrix of order n × n such that |A|=λ, then write the value of |−A|.

A=λ Order of A is n⇒-A=-1n A=-1nλ

If A is a square matrix of order n × n such that $| A | = λ$ , then write the value of |−A|.

$|A| = λ [Order of A is n] \Rightarrow |- A| = {(- 1)}^{n} |A| = {(- 1)}^{n} λ$