Understanding and applying determinants

Only ________ matrices have inverses.

• square

• rectangle

        If A is a square matrix such that 𝐴(𝑎𝑑𝑗 𝐴)  =  8𝐼, where I denotes the identity matrix of the same order, then find the value of|𝐴|.

• 8

• 64

• 2

• NONE OF THESE

       

• Yes.

• No. 

If A and B are invertible matrix then (AB)^-1 =

• A^-1B^-1

• AB

• B^-1A^-1

• none of these

What is the determinant of this matrix and does it have an inverse?

• determinant: 25

  inverse: no

• determinant: 25

  inverse: yes

• determinant: 0

  inverse: no

• determinant: 0

  inverse: yes

The determinant of a matrix is not zero if and only if the matrix has a(n) _____________ .

• inverse

• identity

• scalar

• zero

• 
• 
• 
• Matrix C does not have an inverse

Answer explanation

Matrices that are not square do not have inverses.

What is the inverse of the 2x2 matrix?

• 
• 
• 
• 

What is the inverse of this matrix? Calculate by hand.

• _{(1/25) (-4/25)}

  _{(3/25) (13/25)}

• _{(1/5) (-4/5)}

  _{(3/5) (13/5)}

• _{(6/25) (-2/25)}

  _{(2/25) (9/25)}

• _{(1/150) (-4/150)}

  _{(3/150) (13/150)}

Diketahui matriks S dan M. Jika fungsi  $f\left(S,\ M\right)=S^2-M^2$ , maka matriks  $f\left(S+M,\ S-M\right)$  adalah ....

• (d)

• (b)

• (a)

• (c)

• (e)