Matrices
ICSE · Class 12 · Mathematics
All formulas from Matrices in ICSE Class 12 Mathematics. Key equations, constants, and identities for board exam preparation.
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1) Basic Ideas and Types of Matrices
A = [a_ij]_(m×n)
Number of elements in an m×n matrix = mn
Order of a matrix = m×n
2) Equality, Addition, Subtraction, Scalar Multiplication
Two matrices A and B are equal if A_ij = B_ij for all i, j
(A+B)_ij = A_ij + B_ij
(A-B)_ij = A_ij - B_ij
(kA)_ij = kA_ij
3) Matrix Multiplication and Powers
(AB)_ij = Σ(k=1 to n) A_ik B_kj
Order of AB = m×p
I_m A = A = A I_n
A^0 = I
(AB)C = A(BC)
4) Transpose of a Matrix
(A^T)_ij = A_ji
(A^T)^T = A
(A+B)^T = A^T + B^T
(kA)^T = kA^T
(AB)^T = B^T A^T
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