Question

If A is a square matrix of order 3 such that det(A) = 9, then det(9A⁻¹) is equal to ______.

Options

• 9

• 9²

• 9³

• 9⁴

Answer 1

If A is a square matrix of order 3 such that det(A) = 9, then det(9A⁻¹) is equal to 9².

Explanation:

Given |A| = 9, order of square matrix n = 3

|9 A⁻¹| = 9³|A⁻¹|    ...[From [KA] = Kⁿ|A|]

= `9^3 xx 1/|A|   ...[∵ |A^(−1)| = 1/(|A|)]`

= `9^3 xx 1/9`

= 9²