Question

If A is a square matrix of order 2 such that det (A) = 4, then det (4 adj A) is equal to ______.

Options

• 16

• 64

• 256

• 512

Answer 1

If A is a square matrix of order 2 such that det (A) = 4, then det (4 adj A) is equal to 64.

Explanation:

det (4 adj A) = 4ⁿ det (adj A)

Using det (KB) = Kⁿ det B

Since, n = 2

det (4 adj A) = `4^2 (det A)^(n – 1)`

= `16 xx 4^(2 - 1)`

= `16 xx 4^1`

= 64