Q17 of 127 Page 122

Let A be a non-singular square matrix of order 3 × 3. Then |adj A| is equal to

For a square matrix of order n×n,

We know that |AdjA| = |A|^n-1

So, |AdjA| = |A|^(3-1) = |A|²

For the matrix

Show that A³– 6A² + 5A + 11 I = O. Hence, find A^–1.

If Verify that A³ – 6A² + 9A – 4I = O and hence find A^-1.

If A is an invertible matrix of order 2, then det (A^–1) is equal to

Write Minors and Cofactors of the elements of following determinants: