ors of the matrix, which is the same as the maximum number of linearly independent column vectors.[10] Equivalently it is the dimension of the image of the linear map represented by A.[11] The rank-nullity theorem states that the dimension of the kernel of a matrix plus the rank equals the number of columns of the matrix.[12]සමචතුරස්‍රාකාර න්‍යාස[සංස්කරණය]A square matrix is a matrix with the same number of rows and columns. An n-by-n matrix is known as a square matrix of order n. Any two square matrices of the same order can be added and multiplied. A square matrix A is called invertible or non-singular if there exists a matrix B such thatAB = In.[13]This is equivalent to BA = In.[14] Moreover, if B exists, it is unique and is called the inverse matrix of A, denoted A−1.The entries Ai,i form the main diagonal of a matrix. The trace, tr(A) of a square matrix A is the sum of its diagonal entries. While, as mentioned above, matrix multiplication is not commutative, the trace of the