transcendency said:I'm quite sure that if B = B2, then B must be a diagonal matrix with entries being either 1 or 0, but I don't know how to prove it.
To solve for invertibility of (B+I) given B=B^2, we can use the properties of matrices and apply the determinant rule. This involves finding the determinant of (B+I) and showing that it is non-zero, which indicates that the matrix is invertible.
The determinant rule states that for a square matrix A, if the determinant of A is non-zero, then A is invertible. In other words, a matrix is invertible if and only if its determinant is non-zero.
Determining the invertibility of a matrix is important because it tells us whether or not we can find an inverse matrix for the given matrix. Inverse matrices are useful in solving systems of equations and performing other mathematical operations.
Yes, (B+I) can still be invertible even if B=B^2. This is because the determinant of (B+I) is not affected by the fact that B=B^2. As long as the determinant is non-zero, the matrix is invertible.
Yes, besides using the determinant rule, we can also use the row reduction method to determine the invertibility of a matrix. This involves performing row operations on the matrix and checking if it can be reduced to the identity matrix, which is an indication of invertibility.