Transfering ether between accounts on private testnetwork

I have setup couple of accounts (A and B) in private test net in my local computer. I got 130 ether in account A (somehow), now i want to transfer some ether (lets say 10) to account B. How do i do that. I tried following command. TX is sucessful, but i do not see change in ether in either of accounts.

eth.sendTransaction({from:"Account A", to:"Account B", value: web3.toWei(10, "ether")})

Do i need to some mining here ?
I tried that as well using following command.
Method 1:
geth --mine -rpccorsdomain "*" --ipcapi "admin,eth,miner" --rpcapi "eth,web3" --networkid 1234 -maxpeers 0 --minerthreads 1
Method 2:

I0124 12:13:56.396353 4887 backend.go:331] Automatic pregeneration of ethash DAG ON (ethash dir: /root/.ethash)
I0124 12:13:56.396450 4887 backend.go:338] checking DAG (ethash dir: /root/.ethash)
I0124 12:13:56.396535 4887 miner.go:119] Starting mining operation (CPU=8 TOT=9)

(It shows commint new work on block 27 with 1 txs)
> I0124 12:13:56.397614 4887 worker.go:570] commit new work on block 27 with 1 txs & 0 uncles. Took 975.237µs
I0124 12:13:56.397779 4887 ethash.go:220] Generating DAG for epoch 0 (size 1073739904) (0000000000000000000000000000000000000000000000000000000000000000)
I0124 12:13:57.374453 4887 ethash.go:237] Done generating DAG for epoch 0, it took 976.685021ms

> miner.stop()
I still see no change in account balances for both accounts.

> web3.fromWei(eth.getBalance("Account A"), "ether")
> web3.fromWei(eth.getBalance("Account B"), "ether")

Number of blocks, its showing as 26.
> eth.blockNumber

Please help.
Much appreciate if you could give me sequence of steps that need to be performed.

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