Question

chapter : determinants ​

Answer 1

Step-by-step explanation:

Correct option is

A

∣A∣A

As A is a non-singular matrix, A is invertible and A

−1

=

∣A∣

adjA

⇒adjA=∣A∣A

−1

=B(say).

Now,

adj(adjA)=adj(B)=∣B∣B

−1

=

∣

∣

∣

∣A∣A

−1

∣

∣

∣

(∣A∣A

−1

)

−1

=∣A∣

3

∣A

−1

∣∣A∣

−1

(A

−1

)

−1

[using scalar multiple property of determinants]

=∣A∣

3

∣A∣

1

.

∣A∣

1

A=∣A∣A

Answer 2

•DETERMINATES

A determinant is a number that can be calculated for only squaA or |A|. For every square matrix, ] of order n, we can associate a number with either real number or complex number, called the determinant of the square matrix.

•Singular and Non-singular Matrix:

A matrix is said to be a square matrix if the value of the determinants corresponds to the square matrix is zero. Otherwise, the matrix is called the non-singular matrix