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noelo2014
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Homework Statement
let A and B be nXn invertible matrices. Show that (A.B)^{T} is invertible by finding it's inverse
Homework Equations
The Attempt at a Solution
(A.B)^{T}=B^{T}.A^{T}
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A matrix is considered invertible if there exists another matrix that, when multiplied, results in the identity matrix (a matrix with ones on the main diagonal and zeros everywhere else). In other words, the inverse matrix "undoes" the original matrix.
There are a few ways to determine if a matrix is invertible. One way is to calculate the determinant of the matrix. If the determinant is non-zero, then the matrix is invertible. Another way is to use the row reduction method to see if the matrix can be transformed into the identity matrix. If it can, then the matrix is invertible.
If a matrix is not invertible, it is considered singular. This means that there is no way to "undo" the matrix and obtain the identity matrix. In terms of practical applications, this can mean that the system of equations represented by the matrix has no unique solution.
No, a matrix is either invertible or not. There is no concept of partial invertibility.
No, only square matrices can be invertible. This means that the number of rows is equal to the number of columns. Non-square matrices are not invertible.