0
Yes.
Let M be an arbitrary square matrix and Z be a zero matrix of the same dimension.
Then Z*M = Z = 0*M = 0 => Z = 0.
Z is a scalar matrix with lamda = 0.
Just a note on separate Qs & As here. I'd stumbled on this group because as I can't understand matrices, I wasn't looking deliberately, but it looks as if another questioner had already attracted the answer "No" to the same question, albeit with the words reversed.
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