Question

If A is a square matrix of order 3 such that the value of |adj. A| = 8, then the value of |A^T| is ________.

Options

• `sqrt2`

• `-sqrt2`

• 8

• `2sqrt2`

Answer 1

If A is a square matrix of order 3 such that the value of |adj. A| = 8, then the value of |A^T| is `bbunderline(2sqrt2)`.

Explanation:

We know that 

|adj A| = |A|^n-1

where n is the order of square matrix A

Given |adj. A| = 8

∴ |A|^n-1 = 8

⇒ |A|^3-1 = 8

⇒ |A|² = 8

⇒ |A| = `2sqrt2`

Also, determinant of a matrix and its transpose has same values.