Prove that the product of the matrices `[[cos^2alpha, cosalphasinalpha],[cosalphasinalpha,sin^2alpha]]` and `[[cos^2beta,cosbetasinbeta],[cosbetasinbeta,sin^beta]]` is the null matrix when `alpha and beta` differ by an odd multiple of `pi/ 2`.

Provet that the producet of the matrics [[cos^2 alpha cos alpha sin alpha], [ cos alpha sin alpha sin^2 alpha]] and [[cos^2 beta cos beta sin beta], [ cos beta sin beta sin^2 beta]] is the null matrix when alpha and beta differ by an odd multiple of pi / 2 .

Prove that the product of the matrices {:[(cos ^(2)alpha,cos alpha sin alpha ),(cos alpha sinalpha, sin^(2)alpha)]and {:[(cos ^(2)beta,cosbetasinbeta),(cos betasinbeta,sin^(2)beta)] is the null matrix when alpha and beta differ by an odd multiple of (pi)/(2) .

If neither alpha nor beta is a multiple of pi/2 and the product AB of matrices A=[(cos^2alpha, cosalpha sin alpha),(cosalpha sinalpha, sin^2alpha)] and B=[(cos^2beta, cosbeta sinbeta),(cosbetasinbeta, sin^2beta)] is a null matrix then alpha- beta is (A) 0 (B) an odd mutiple of pi/2 (C) a multiple of pi (D) none of these

{:A=[(cos^2 alpha,cosalphasinalpha),(cosalphasinalpha,sin^2alpha)]:} {:B=[(cos^2 beta,cosbetasinbeta),(cosbetasinbeta,sin^2beta)]:} are two matrices such that the product AB is the null matrix, then (alpha-beta) is

If A=[(cos^(2)alpha, cos alpha sin alpha),(cos alpha sin alpha, sin^(2)alpha)] and B=[(cos^(2)betas,cos beta sin beta),(cos beta sin beta, sin^(2) beta)] are two matrices such that the product AB is null matrix, then alpha-beta is

If A=[(cos^(2)alpha, cos alpha sin alpha),(cos alpha sin alpha, sin^(2)alpha)] and B=[(cos^(2)betas,cos beta sin beta),(cos beta sin beta, sin^(2) beta)] are two matrices such that the product AB is null matrix, then alpha-beta is

If A=[(cos^(2)alpha, cos alpha sin alpha),(cos alpha sin alpha, sin^(2)alpha)] and B=[(cos^(2)betas,cos beta sin beta),(cos beta sin beta, sin^(2) beta)] are two matrices such that the product AB is null matrix, then alpha-beta is

If A=[(cos^(2) alpha, cos alpha sin alpha),(cos alpha sin alpha,sin^(2)alpha)] and B=[(cos^(2) beta, cos beta sin beta),(cos beta sin beta, sin^(2) beta)] are two matrices such that the product AB is the null matrix then alpha-beta is

If A=((cos^(2)alpha , cos alpha sin alpha),(cos alpha sin alpha, sin^(2)alpha)) and B=((cos^(2)beta , cos betasin beta),(cosbeta sin beta,sin^(2)beta)) are two matrices such that the product AB is the null matrix then alpha - beta =