Let A=[{:(" "2,3,5),(-1,0,4):}]" and "B=...

Let `A=[{:(" "2,3,5),(-1,0,4):}]" and "B=[{:(4,-2,3),(2," "6,-1):}].`
Verify that `A+B=B+A.`

Text Solution

Verified by Experts

Here, A is a `2xx3` matrix and B is a `2xx3` matrix. So, A and B are comparable.
Therefore, `(A+B)` and `(B+A)` both exist and each is a `2xx3` matrix.
Now, `A+B=[{:(" "2,3,5),(-1,0,4):}]+[{:(4,-2," "3),(2," "6,-1):}]`
`=[{:(2+4,3+(-2),5+3),(-1+2,0+6,4+(-1)):}]=[{:(6,1,8),(1,6,3):}].`
And, `B+A=[{:(4,-2," "3),(2," "6,-1):}]+[{:(" "2,3,5),(-1,0,4):}]`
`=[{:(4+2,-2+3,3+5),(2+(-1)," "6+0,(-1)+4):}]=[{:(6,1,8),(1,6,3):}].`
Hence, `A+B=B+A.`

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RS AGGARWAL-MATRICES-Exercise 5F

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If A=[{:(2,3),(4,5):}], show that (A-A') is skew-symmetric.
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