If A is a matrix and k is a scalar; then `(kA)^T = k(A^T)`

A square matrix A is said to be orthogonal if A^T A=I If A is a sqaure matrix of order n and k is a scalar, then |kA|=K^n |A| Also |A^T|=|A| and for any two square matrix A d B of same order \AB|=|A||B| On the basis of abov einformation answer the following question: If A is an orthogonal matrix then (A) A^T is an orthogonal matrix but A^-1 is not an orthogonal matrix (B) A^T is not an orthogonal mastrix but A^-1 is an orthogonal matrix (C) Neither A^T nor A^-1 is an orthogonal matrix (D) Both A^T and A^-1 are orthogonal matices.

A square matrix A is said to be orthogonal if A^T A=I If A is a square matrix of order n and k is a scalar, then |kA|=K^n |A| . Also |A^T|=|A| and for any two square matrix A and B of same order \|AB|=|A||B| On the basis of above information answer the following question: If A=[(p,q,r),(q,r,p),(r,p,q)] be an orthogonal matrix and pqr=1, then p^3+q^3+r^3 may be equal to (A) 2 (B) 1 (C) 3 (D) -1

A square matrix A is said to be orthogonal if A^T A=I If A is a square matrix of order n and k is a scalar, then |kA|=K^n |A| Also |A^T|=|A| and for any two square matrix A d B of same order \AB|=|A||B| On the basis of above information answer the following question: IF A is a 3xx3 orthogonal matrix such that |A|=1, then |A-I|= (A) 1 (B) -1 (C) 0 (D) none of these

A square matrix A is said to be orthogonal if A^T A=I If A is a sqaure matrix of order n and k is a scalar, then |kA|=K^n |A| Also |A^T|=|A| and for any two square matrix A d B of same order \AB|=|A||B| On the basis of abov einformation answer the following question:If A=[(1,1),(0,1)] and P is a orthogonal martix and B=PAP^T, P^TB^2009 P= (A) [(1,2009),(0,1)] (B) [(1,2009),(2009,1)] (C) [(1,0),(2009,1)] (D) [(1,0),(0,1)]

Let A be a square matrix and k be a scalar. Prove that (i) If A is symmetric, then kA is symmetric. (ii) If A is skew-symmetric, then kA is skew-symmetric.

Assertion (A) : If every element of a third order determinant of value Delta is multiplied by 5, then the value of the new determinant is 125Delta . Reason (R ) : If k is a scalar and A is an nxxn matrix, then |kA|=k^(n)|A|

If A is a square matrix of order n xx n and k is a scalar, then adj (kA) is equal to (1) k adj A (2) k^n adj A (3) k^(n-1) adj A (4) k^(n+1) adj A

If A is square matrix, A+A^(T) is symmetric matrix, then A-A^(T) =

If A is a matrix of order 3times3 then |KA|=K^(n)|A| where n is

If A is a nonsingular matrix such that A A^(T)=A^(T)A and B=A^(-1) A^(T) , then matrix B is