Module 2: Special Square Matrices

Question 1

If A and B are square matrix such that AB = BA

Answer 1

Commute matrix

Question 2

If A and B are such that AB = - BA

Answer 2

Anti-commute matrix

Question 3

A matrix A which A k+1 = A, where k is a positive integer, is called ________

Answer 3

Periodic

Question 4

If k is the least positive integer for which A k+1 = A,
then A is said to be of period k. IF k = 1, so that A2 = A, then A is called __________

Answer 4

Idempotent

Question 5

A matrix A for which A p = 0, where p is a positive integer,

Answer 5

Nilpotent

Question 6

A matrix A such that A2 = I is called __________

Answer 6

Involutory

Question 7

symmetric. A square matrix A such that AT

= - A is called _________________

Answer 7

Skew-symmetric

Question 8

The complex numbers a + bi and a – bi are called _________

Answer 8

Conjugate, “Ā”

Question 9

The transpose of the conjugate of the matrix A is the _________ of the matrix;

Answer 9

Tranjugate, “A*”

Question 10

A square matrix A = [ aij ] such that ̅A̅̅T̅ = A is called _________.

Answer 10

Hermitian

Question 11

A square matrix A = [ aij ] such that ̅A̅̅T̅ = −A is called _____________

Answer 11

Skew-hermitian

Question 12

.If the inverse of a matrix is equal to its transpose, the matrix is referred to as an ___________ matrix

Answer 12

Orthogonal