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Prove that the product of the matrices [...

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`.

A

null matrix

B

unit matrix

C

diagonal matrix

D

orthogonal matrix

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The correct Answer is:
A
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MCGROW HILL PUBLICATION-MATRICES-SOLVED EXAMPLES ( LEVEL 1 ( Single Correct Answer Type Questions ) )
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  2. If A is an invertible matrix and B is an orthogonal matrix of the orde...

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  3. Prove that the product of the matrices [[cos^2alpha, cosalphasinalpha]...

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  4. If [(2,1),(7,4)]A[(-3,2),(5,-3)]=[(1,0),(0,1)] then matrix A equals

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  5. The matrix A satisfying A[[1, 5], [0, 1]]=[[3, -1], [6, 0]] is

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  6. If product of matrix A with [(1,1),(2,0)] is [(3,2),(1,1)] then A^(-1)...

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  7. If A and B are two skew symmetric matrices of order n then

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  8. Which of the following statements is false :

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  9. If A and B are symmetric matrices then A B-B A is a Symmetric Matrix ...

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  10. Let A and B be two 3xx3 matrices such that A+B = 2 B' and 3A + 2B= I ...

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  11. If A and B are two nonzero square matrices of the same order such that...

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  12. If A is skew-symmetric and B=(I-A)^(-1)(I+A), then B is

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  13. Let a(n)=3^(n)+5^(n), nin N and let A=((a(n),a(n+1),a(n+2)),(a(n+1)...

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  14. First row of a matrix A is [1,3,2]. If adj A=[(-2,4,alpha),(-1,2,1),...

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  15. Suppose ABC is a triangle with sides a,b ,c and semiperimeter s. Then ...

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  16. The number of matrices A = [(a,b),(c,d)] ( where a,b,c,din R ) such...

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  17. Let A be a 3xx3 matrix with entries from the set of numbers, If the sy...

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  18. A=[{:(a,b),(b,-a):}] and MA=A^(2m), m in N for some matrix M, then whi...

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  19. Let A=[(a,b),(c,d)]be a 2 xx 2 matrix, where a, b, c, d take value 0 t...

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  20. Find the inverse of each of the matrices given below : Let D= "dia...

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