Here are some of the most important points from matrices to be understood and remembered by EAMCET aspirants.

Product of two upper triangular matrices is a upper triangular matrix.

Determinant of triangular matrix is the product of the elements in the principle diagonal.

(i) trace (KA) = K tr(A) (ii) tr (A + B) = tr(A) + tr(B) (iii) tr (AB) = tr (BA)

If A is a skew symmetric matrix then, 1-> All the elements in the principle diagonal are equal to zero. 2-> |A|≠ 0 then its order is an odd number.

If A, B are symmetric matrices, K is a scalar then (i) KA is symmetric. (ii) (A + B) and (A – B) are symmetric. (iii) AB, BA are symmetric if and only if AB = BA.

For any square matrix A, (A + A^{T}) is symmetric and (A – A^{T}) is skew symmetric.

A is a matrix of order m x n then A.A^{T}, A^{T}.A are symmetric matrices.

The only non-singular idempotent matrix is the unit matrix. That is if A^{2} = A and A ≠ I then |A| = 0

If A, B are square matrices of the same type satisfying the condition AB = A, BA = B then (i) Both A and B are idempotent matrices (ii) For any natural number ‘n’, (A+B)^{n} = 2^{(n-1)} (A+B)

If A is an involutary matrix then,

If A is an orthogonal matrix then,

Determinant of A is ±1. If the rays are in right handed system then the value of determinant is +1 and if they are in left handed system then the value is -1.