Question

If A is a square matrix of order 3, such that A(adj A) = 10I, then |adj A| is equal to ______.

Options

• 1

• 10

• 100

• 101

Answer 1

If A is a square matrix of order 3, such that A(adj A) = 10I, then |adj A| is equal to 100.

Explanation:

Consider the equation

A(adj A) = |A|I

Here, A(adj A) = 10I

Then, |A| = 10

Since, |adj A| = |A|^{n – 1}

Where n is order of matrix

Here, |A|^{3 – 1}

= 10²

= 100