If A and B are non-singular matrices of the same order, write whether AB is singular or non-singular.

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Solution

Let A & B be non-singular matrices of order n.

$|A| \neq 0 and |B| \neq 0 [By definition] Since they are of same order, |A B| = |A| |B| |A B| = 0 iff either |A| = 0 or |B| = 0 But it is not the case here . Thus, |A B| is non - zero and A B is non - singular matrix .$

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If A and B are non-singular matrices of the same order, write whether AB is singular or non-singular.

Let A & B be non-singular matrices of order n. A≠0 and B ≠0 By definition Since they are of same order, AB=ABAB=0 iff either A=0 or B=0 But it is not the case here. Thus, AB is non-zero and AB is non-singular matrix.

Let A & B be non-singular matrices of order n.

$|A| \neq 0 and |B| \neq 0 [By definition] Since they are of same order, |A B| = |A| |B| |A B| = 0 iff either |A| = 0 or |B| = 0 But it is not the case here . Thus, |A B| is non - zero and A B is non - singular matrix .$