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Two matrices are said to be equal if they have the same order and their corresponding elements are equal. e.g., then a = 1, b = 2, c = 3, d = 4, e = 5 and f = 6...

\ A + B = B + A \ A + B = B ..

From (1) and (2), (A + B) + C = A + (B + C) \ The associative law is verifi..

skew-symmetric for every square matrix A. That is any square matrix is expressible as the sum of a symmetric matrix and a skew-symmetric matrix. 5. A matrix which is both symmetric and skew symmetric is a zero matr..

The matrices are identify matrices of order 2 and 3 respectivel..

The number of combinations of n dissimilar things, taken r at a time is..

1. O!= 1 2. When n is a negative or fraction, n! is not defined...

The number of permutations of n dissimilar things taken r ..

1. If a, x, b are in A.P, then x is called the arithmetic mean (A.M.) between the extremes a and b. 2. a. To insert n arithmetic means between two given quantities. Let a and b be any two given quantities, and let A 1 ,A 2 ,A 3 ,-----A n be n arithmetic means to be inserted between a and b so that ..

Let S n = 1+2+3+4+...+n This series is an A.P. Here a=1, d=1, l = t n = n 2. To find the sum to squares of first n natural numbers. or..