Q17 of 127 Page 131

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 a = [ ccc 2&-1&1 -1&2&-1 1&-1&2 ] 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

Examine the consistency of the system of equations.

x + 2y = 2

2x + 3y = 3