No, matrices are associative, A(BC) = (A B)C, but they are not always commutative.PotentialE said:I forgot the associative property is non-applicable to matrices.
The transpose of a matrix is a new matrix in which the rows of the original matrix are now the columns, and the columns are now the rows. This means that the elements of the first row of the original matrix will become the first column of the transposed matrix, and so on.
To calculate the transpose of a matrix, simply switch the rows and columns of the original matrix. For a matrix with dimensions m x n, the transposed matrix will have dimensions n x m. You can also use the transpose function in most programming languages to calculate the transpose of a matrix.
An inverse matrix is a matrix that, when multiplied by the original matrix, results in the identity matrix. The identity matrix is a square matrix with 1s along the main diagonal and 0s everywhere else. In other words, an inverse matrix "undoes" the effects of the original matrix.
To find the inverse of a matrix, you can use the Gauss-Jordan elimination method or use a matrix calculator. The Gauss-Jordan elimination method involves performing row operations on the original matrix until it is reduced to the identity matrix, with the same operations performed on an identity matrix to get the inverse. Matrix calculators use algorithms to find the inverse directly.
No, not every matrix can be inverted. A matrix can only be inverted if it is a square matrix (same number of rows and columns) and has a non-zero determinant. If a matrix cannot be inverted, it is known as a singular or non-invertible matrix.