State True or False for the statements |A -1 | ≠ |A| -1 , where A is non-singular matrix.

Question

Philoid · Accepted Answer

False

Given A is non-singular matrix.

We know that AA^-1 = I.

⇒|A||A^-1| = 1

∴ |A^-1| = 1/|A| = |A|^-1