- #1
Dustinsfl
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If AB=I, then A is invertible.
False, but not sure how to show it.
False, but not sure how to show it.
There's no requirement that A and B have to be square matrices. I came up with a 2x3 matrix and a 3x2 matrix whose product is I, a 2x2 matrix, yet neither of the matrices in the product is invertible.Dustinsfl said:If AB=I, then A is invertible.
False, but not sure how to show it.
If two square matrices, A and B, when multiplied together result in the identity matrix (I), then the matrix A is said to be invertible. This means that there exists a matrix B' such that when multiplied by A, it results in the identity matrix.
No, the statement is not always true. In order for A to be invertible, B must also be invertible. If B is not invertible, then A cannot be invertible even if their product is the identity matrix.
Yes, consider the following matrices: A = [1 2; 3 6] and B = [2 -1; -1 0]. When multiplied together, AB = [0 1; 0 1] = I. However, A is not invertible since its determinant is 0.
A square matrix is invertible if its determinant is non-zero. If the determinant is 0, then the matrix is not invertible. Additionally, you can check if the matrix has an inverse by using Gaussian elimination or finding the inverse using the adjugate matrix.
No, both matrices must be square for the statement to hold. If the matrices are of different sizes, then the product AB will not result in the identity matrix and therefore, A cannot be invertible.