Matrices & Prop...

Multiplication of real valued square matrices of same dimension is

If a matrix A is Symmetric as well as Skew-Symmetric, then:

If A is a skew-symmetric matrix, then A² is

lf the order of A is 4 × 3, the order of B is 4 × 5 and the order of C is 7 × 3, then the order of (A^TB)^T C ^T is

If \({\rm{A}} = \left[ {\begin{array}{*{20}{c}} 0&1\\ 1&0 \end{array}} \right]\), then the value of A⁴ is

Consider the following question and decide which of the statements is sufficient to answer the question.

Find the value of n, if

Statements∶

1. AB = A

2. \(A\; = \;\left[ {\begin{array}{*{20}{c}} n&9\\ 2&1 \end{array}} \right] , B\; = \;\left[ {\begin{array}{*{20}{c}} 1&0\\ 0&1 \end{array}} \right]\)

A square matrix A is called orthogonal if_______ where A’ is the transpose of A.

If \(A = \left[ {\begin{array}{*{20}{c}} 3&2&5\\ 4&1&3\\ 0&6&7 \end{array}} \right] = \frac{1}{2} \cdot (P + Q)\) where P is symmetric and Q is skew symmetric matrix then P and Q are ?

If a matrix has p elements, where is p a prime then what is the number of possible orders it can have ?

Which one of the following matrices is an elementary matrix?