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If A is a square mastrix, then...

If A is a square mastrix, then

A

`A+A^(T)` is symmetric matrix

B

`"AA"^(T)` is skew- symmetric matrix

C

`A^(T)+A` is skew- symmetric matrix

D

`A^(T)A` is skew -symmetric matrix

Text Solution

Verified by Experts

The correct Answer is:
A
Now `(A+A^(T))^(T)=A^(T)+(A^(T))^(T)=A^(T)+A`
`:.A+A^(T)` is symmetric matrix.
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-MATRICES-MHT CET CORNER
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  3. If A=[(2,2),(-3,2)], B=[(0,-1),(1,0)] then (B^(-1)A^(-1))^(-1) is equa...

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  4. If matrix A=[(1,2),(4,3)], such that AX=l, then X is equal to

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  5. The multiplicative inverse of A = [(cos theta,-sin theta),(sin theta,c...

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  6. The value of a for which system of equation , a^3x+(a+1)^3y+(a+2)^3z=0...

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  7. Let A=[(cos theta, -sin theta),(- sin theta,-cos theta)] then the inve...

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  8. If matrix A=[(a,b),(c,d)], then |A|^(-1) is equal to

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  9. If A=[(3,2,4),(1,2,1),(3,2,6)] and A(ij) are the cofactors of a(ij), t...

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  10. A=[(cos theta, -sin theta),(sin theta, cos theta)] and AB=BA=l, then B...

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  11. The inverse matrix of A=[(0,1,2),(1,2,3),(3,1,1)] is

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  12. The solutiion of (x,y,z) the equation [(-1,0,1),(-1,1,0),(0,-1,1)][(x)...

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  13. For the system of equaltions : x+2y+3z=1 2x+y+3z=2 5x+5y+9z=4

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  14. If A=[(cos^(2)alpha, cos alpha sin alpha),(cos alpha sin alpha, sin^(2...

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  15. If A(alpha)=[(cos alpha, sin alpha),(-sin alpha, cos alpha)] then the ...

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  16. If A=[(1,-1),(2,-1)] and B=[(1,a),(4,b)] and (A+B)^(2)=A^(2)+B^(2). ...

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  17. If A+I=[(3,-2),(4,1)] then (A+I)(A-I) is equal to

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  18. If A=[(x,y,z)],B=[(a,h,g),(h,b,f),(g,f,c)] and C=[(x),(y),(z)] Then ...

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  19. If A=[(-2,4),(-1,2)] then A^(2) is equal to

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