If A is a square matrix then orthogonality property mandates

Concept:

Orthogonal matrix: When the product of a matrix to its transpose gives identity matrix.

Suppose A is a square matrix with real elements and of n x n order and AT or A’ is the transpose of A.

AAT = I

Important Points

• A square matrix such that A2 = I is called the involuntary matrix.
• A square matrix such that A2 = A is called the Idempotent matrix.
• Any square matrix A is said to be non-singular if |A| ≠ 0, and a square matrix A is said to be singular if |A| = 0.
• A square matrix A = [aij] is said to be Hermitian matrix if aij = a̅ij