线性代数证明题,if AandB are （n×n）matrices such that A is nonsingula

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线性代数证明题,
if AandB are （n×n）matrices such that A is nonsingular and AB=0,then prove that B=0.[hint writeB=[b1……bn]and consider AB=[AB1……ABn]]

obin答的没错.
不过从你给的提示看,好像不能用A可逆,而让从线性方程组的角度考虑.
记法如提示.
由 AB=0 知 [Ab1,Ab2,...,Abn]=0
所以 Abi = 0,i=1,2,...,n
所以 bi 都是齐次线性方程组 Ax=0 的解向量 ( i=1,2,...,n)
再由已知A非奇异,Ax=0 只有零解,所以 bi=0,i=1,2,...,n
故 B=0.

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