Question

Question(6)
If A is a 4 x 4 matrix and det (Adj A) = - 27 then det A =​

Answer 1

Solution :

det ( Adj A ) = | A |^n-1

Given

det ( Adj A ) = - 27

| A |^n-1 = - 27

n = 4 (matrix)

| A |^4-1 = - 27

| A |^3 = - 27

| A | = - 3

Answer

$\boxed{\bold{det A = - 3}}$

Answer 2

Step-by-step explanation:

Solution :

det ( Adj A ) = | A |^n-1

Given

det ( Adj A ) = - 27

| A |^n-1 = - 27

n = 4 (matrix)

| A |^4-1 = - 27

| A |^3 = - 27

| A | = - 3

Answer

$\boxed{\bold{det A = - 3}} detA=−3$