Question

If A is a non-singular square matrix of order 3 such that A^2 = 3A, then
value of det.A is

(A) -3
(B) 3
IAL
(C) 9
D) 27​

Answer 1

$\textbf{Concept:}$

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

$\boxed{\bf\,det(AB)=det(A)\,det(B)}$

$\text{If A is a square matrix of order n, then}$

$\boxed{\bf\,det(kA)=k^n\;det(A)}$

$\textbf{Given:}$

$A^2 = 3A$

$\textbf{To find:}\;det(A)$

$\text{Now,}$

$A^2 = 3A$

$det(A^2) = det(3A)$

$det(AA) = det(3A)$

$det(A)\;det(A) = 3^3det(A)$

$\implies\boxed{\bf\,det(A) = 27}$

$\therefore\textbf{The value of det(A) is 27}$

$\implies\bf\;\textbf{option (D) is correct}$

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