NCERT Solutions for Class 12 Mathematics Chapter 3 Matrices

Short Note:

• Matrices are classified by their order and structure into row, column, square, diagonal, scalar, and identity matrices, each with distinct properties.

• Matrix addition and subtraction require matrices of the same order, while matrix multiplication requires the number of columns of the first matrix to equal the number of rows of the second.

Short Note:

• The transpose of a matrix A, denoted A', is obtained by interchanging its rows and columns; A is symmetric if A = A' and skew-symmetric if A' = -A.

• Any square matrix A can always be expressed as the sum of a symmetric matrix ½(A + A') and a skew-symmetric matrix ½(A - A').

Short Note:

• Elementary row/column operations — swapping rows, multiplying a row by a nonzero scalar, or adding a multiple of one row to another — are used to simplify matrices and find inverses.

• A square matrix A has an inverse only if it is non-singular (|A| ≠ 0); the inverse can be computed using elementary operations or the adjoint method.