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

Question

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

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

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