Matrices Question
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Grade 12 Matrices CCSS: HSN-VM.C.10
If A is a given square matrix, and it is known that there exists a matrix B such that AB=1, which of the following would be the most efficient ways to find the matrix B?
- Find the inverse of A. This is the matrix B.
- Find the transpose of A. This is the matrix B.
- Create a matrix B whose elements are variables. Then, perform matrix multiplication with the matrix A, setting each resulting entry equal to one. Solve this system of equations, which will give the elements of matrix B.
- Multiply both sides of the equation, on the left, by slight variations of the matrix A. When one of these matrices, multiplied by A, becomes the identity matrix, this is the matrix B.