Unitary Matrix:
A square matrix A is said to be unitary if its conjugate transpose A* is equal to its inverse A^-1. In other words, A* A = I, where A* represents the conjugate transpose of A.

Explanation:
To understand why a unitary matrix satisfies the given condition, let's consider a square matrix A and its conjugate transpose A*. The product of A* and A can be written as:
A* A = (A^H)(A)

Here, A^H represents the conjugate transpose of A. If A is a unitary matrix, then A^H = A^-1. Therefore, we can rewrite the product as:
A* A = (A^-1)(A)

Using the properties of matrix multiplication, we know that when a matrix is multiplied by its inverse, the result is the identity matrix. Thus, we have:
A* A = I

Therefore, a square matrix A is considered unitary if its conjugate transpose multiplied by itself is equal to the identity matrix.

Example:
Let's consider a 2x2 matrix A:
A = [a b]
[c d]

To check if A is unitary, we need to calculate A* A and see if it equals the identity matrix I.
A* = [a* c*]
[b* d*]

A* A = [a* c*] [a b]
[b* d*] [c d]

Multiplying the matrices, we get:
A* A = [a*a + c*b a*b + c*d]
[b*a + d*b b*b + d*d]

If A* A is equal to the identity matrix I, then:
a*a + c*b = 1
a*b + c*d = 0
b*a + d*b = 0
b*b + d*d = 1

Solving these equations simultaneously, we can find the values of a, b, c, and d that satisfy the condition for a unitary matrix.

Conclusion:
In summary, a square matrix A is said to be unitary if its conjugate transpose multiplied by itself is equal to the identity matrix. This condition ensures that the matrix is invertible and has properties that are useful in various mathematical applications.