If A = [[1, 0], [0, 1]] is the identity matrix, what is A^n for any integer n?
Practice Questions
1 question
Q1
If A = [[1, 0], [0, 1]] is the identity matrix, what is A^n for any integer n?
A
0
I
None of the above
A^n = I for any integer n, where I is the identity matrix.
Questions & Step-by-step Solutions
1 item
Q
Q: If A = [[1, 0], [0, 1]] is the identity matrix, what is A^n for any integer n?
Solution: A^n = I for any integer n, where I is the identity matrix.
Steps: 6
Step 1: Understand what the identity matrix is. The identity matrix A = [[1, 0], [0, 1]] is a special matrix that, when multiplied by any other matrix of the same size, leaves that matrix unchanged.
Step 2: Recognize that raising a matrix to a power means multiplying the matrix by itself that many times. For example, A^2 means A multiplied by A.
Step 3: Calculate A^1. Since A is the identity matrix, A^1 = A = [[1, 0], [0, 1]].
