If A is a singular matrix, then adj A is
(a) non-singular
(b) singular
(c) symmetric
(d) not defined

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Solution

(b) singular

$A is singular, so |A| = 0 . By definition, we have A adj (A) = O \Rightarrow |A adj (A)| = |O| \Rightarrow |A| |adj (A)| = 0 \Rightarrow |adj (A)| = 0 Hence, adj (A) is singular .$

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If A is a singular matrix, then adj A is (a) non-singular (b) singular (c) symmetric (d) not defined

(b) singular A is singular, so A =0.By definition, we haveAadj A =O ⇒A adj A=O⇒A adj A =0 ⇒adj A =0 Hence, adj A is singular.

If A is a singular matrix, then adj A is
(a) non-singular
(b) singular
(c) symmetric
(d) not defined

(b) singular

$A is singular, so |A| = 0 . By definition, we have A adj (A) = O \Rightarrow |A adj (A)| = |O| \Rightarrow |A| |adj (A)| = 0 \Rightarrow |adj (A)| = 0 Hence, adj (A) is singular .$