If A is a square matrix of order 3 and |A|=5, | vedclass

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(B) We know that for a square matrix $A$ of order $n$,the property of the adjoint matrix is given by $A 	ext{ adj. } A = |A| I$,where $I$ is the iden

Vedclass · Accepted Answer

$125$

Vedclass · Answer

(B) We know that for a square matrix $A$ of order $n$,the property of the adjoint matrix is given by $A 	ext{ adj. } A = |A| I$,where $I$ is the identity matrix of order $n$. Taking the determinant on both sides,we get $|A 	ext{ adj. } A| = | |A| I |$. Since $|kI| = k^n |I|$ for a matrix of order $n$,we have $|A 	ext{ adj. } A| = |A|^n |I|$. Since $|I| = 1$,the formula becomes $|A 	ext{ adj. } A| = |A|^n$. Given that $n = 3$ and $|A| = 5$,we substitute these values into the formula: $|A 	ext{ adj. } A| = (5)^3 = 125$.

If $A$ is a square matrix of order $3$ and $|A|=5$,then $|A \text{ adj. } A|$ is

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