Question

If A is a 3 × 3 matrix and |A| = 2, then the matrix represented by A (adj A) is equal to. 

Options

• `[(1,0,0),(0,1,0),(0,0,1)]`

• `[(2,0,0),(0,2,0),(0,0,2)]`

• `[(1/2,0,0),(0,1/2,0),(0,0,1/2)]`

• `[(0,2,0),(2,0,0),(2,0,0)]`

Answer 1

`[(2,0,0),(0,2,0),(0,0,2)]`

Explanation:

A (adjA) = A (A^-1 |A|)  ...[∵ A^-1 = `("adj A")/|"A"|`]

= (AA^-1) |A|

= 2 I

∴ A (adj A) = `[(2,0,0),(0,2,0),(0,0,2)]`