What is the inverse of the matrix A = [[0, 1], [1, 0]]?
Practice Questions
1 question
Q1
What is the inverse of the matrix A = [[0, 1], [1, 0]]?
[[0, 1], [1, 0]]
[[1, 0], [0, 1]]
[[0, 0], [0, 0]]
[[1, 1], [1, 1]]
The inverse of A is A itself since A is an involutory matrix.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the inverse of the matrix A = [[0, 1], [1, 0]]?
Solution: The inverse of A is A itself since A is an involutory matrix.
Steps: 8
Step 1: Understand what an inverse of a matrix is. The inverse of a matrix A is another matrix B such that when you multiply A and B, you get the identity matrix.
Step 2: Identify the given matrix A, which is [[0, 1], [1, 0]].
Step 3: Calculate the product of A with itself (A * A).
Step 4: Perform the multiplication: A * A = [[0, 1], [1, 0]] * [[0, 1], [1, 0]].
Step 5: Calculate the result: The first row will be [0*0 + 1*1, 0*1 + 1*0] = [1, 0]. The second row will be [1*0 + 0*1, 1*1 + 0*0] = [0, 1].
Step 6: The result of A * A is [[1, 0], [0, 1]], which is the identity matrix.
Step 7: Since A * A = I (the identity matrix), this means that A is its own inverse.
Step 8: Conclude that the inverse of matrix A is A itself.
