Chapter 5: Matrices

Question 1

Three properties of matrix inverses, if A and B are non-singular nxn matrices

Answer 1

(A^-1)^-1 = A
(AB)^-1 = B^-1A^-1
(A^T)^-1 = (A^-1)^T

Question 2

When are the three properties of matrix inverses true?

Answer 2

If the two matrices are non-singular nxn matrices

Question 3

Is every square matrix invertible?

Answer 3

No. A matrix without an inverse is a singular matrix. If the inverse exists, then AA^-1= identity matrix, I.

Question 4

When can you not invert a matrix?

Answer 4

If it’s determinant is 0

Question 5

What are the three properties of transpose matrices?

Answer 5

(A+B)^T = A^T + B^T
(A^T)^T = A
(AB)^T = B^T A^T