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If A ,Ba n dC three matrices of the sam...

If `A ,Ba n dC` three matrices of the same order, then prove that `A=B rArr A+C=B+C`

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Let `A, B and C` are `m xxn` order matrices such that,
`A = [a_(ij)]_(mxxn)`
`B = [b_(ij)]_(mxxn)`
`C = [c_(ij)]_(mxxn)`
It is given that ,
`A = B`
`=> a_(ij) = b_(ij)` , `1 le i le m and 1 le j le n`
`=> a_(ij) + c_(ij) = b_(ij) + c_(ij)` , ` 1 le i le m and 1 le j le n`
...
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