If A is a singular matrix, then adj A is

Let A be of order n × n.Since          A × adj A = |A| I∴              |A × adj A| = |A|n⇒               |A| |adj A| = |A|n∴              |adj A| = |A|n–1Since A is singular,∴                 |A| = 0.∴                      |adj A| = 0.Hence, adj A is singular.