A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. It is typically used to represent data or perform mathematical operations in linear algebra.
To add or subtract matrices, they must have the same dimensions. Simply add or subtract the corresponding elements in each matrix to get the resulting matrix.
The identity matrix is a square matrix with 1s on the main diagonal and 0s everywhere else. When multiplied with another matrix, the identity matrix behaves like the number 1 in regular arithmetic.
To multiply two matrices, the number of columns in the first matrix must match the number of rows in the second matrix. The resulting matrix will have the same number of rows as the first matrix and the same number of columns as the second matrix.
The inverse of a matrix is a matrix that, when multiplied with the original matrix, gives the identity matrix. Not all matrices have an inverse, and for those that do, the inverse can be found using certain mathematical methods.