Question

If A is a 3*3 matrix then |5A| is equal to

Answer 1

✪ᴀɴsᴡᴇʀ✪

• $|5A| = 5^3|A|$

★ᴇxᴘʟᴀɪɴᴀᴛɪᴏɴ★

Let $A = [ C_1\:\:C_2\:\:C_3]$

where $C_1, C_2, C_3$ are the columns of the 3x3 matrix.

$\implies 5A = 5[ C_1\:\:C_2\:\:C_3]$

$\implies 5A = [ 5C_1\:\:5C_2\:\:5C_3]$

$\implies |5A| = | 5C_1\:\:5C_2\:\:5C_3|$

$\implies |5A| =5| C_1\:\:5C_2\:\:5C_3|$

$\implies |5A| =5^2| C_1\:\:C_2\:\:5C_3|$

$\implies |5A| =5^3| C_1\:\:C_2\:\:C_3|$

$\implies |5A| =5^3|A|$