The blank in the statement “Suppose that A is a square n by n matrix that is nonsingular. The matrix B such that A B = B A = I n is called _____ of the matrix A .”
The blank in the statement “Suppose that A is a square n by n matrix that is nonsingular. The matrix B such that A B = B A = I n is called _____ of the matrix A .”
To fill: The blank in the statement “Suppose that A is a square n by n matrix that is nonsingular. The matrix B such that AB=BA=In is called _____ of the matrix A .”
Expert Solution & Answer
Answer to Problem 5AYU
The complete statement is “Suppose that A is a square n by n matrix that is nonsingular. The matrix B such that AB=BA=In is called inverse of the matrix A .”
Explanation of Solution
Given information:
The statement “Suppose that A is a square n by n matrix that is nonsingular. The matrix B such that AB=BA=In is called _____ of the matrix A .”
Consider the provided statement “Suppose that A is a square n by n matrix that is nonsingular. The matrix B such that AB=BA=In is called _____ of the matrix A .”
When the two matrices are multiplied and follow commutative law of multiplication then one matrix is the inverse of other.
For example: Let A=[1101],B=[1−101] .
Now,
AB=[1101][1−101]=[1001]
And,
BA=[1−101][1101]=[1001]
Therefore, AB=BA=I2 .
So, A=B−1
Thus, the complete statement is “Suppose that A is a square n by n matrix that is nonsingular. The matrix B such that AB=BA=In is called inverse of the matrix A .”
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.