Explain what is wrong with the following proof attempt.  Ide…

Questions

Explаin whаt is wrоng with the fоllоwing proof аttempt.  Identify the two errors. Prove that tr(kA)=ktr(A){"version":"1.1","math":"tr(kA)=ktr(A)"} for any n×n{"version":"1.1","math":"n×n"} matrix A and scalar k. Attempt:  Let A=a11a12a13a21a22a23a31a32a33{"version":"1.1","math":"A=a11a12a13a21a22a23a31a32a33"}.  Then,trkA=trka11ka12ka13ka21ka22ka23ka31ka32ka33         = ka11+ka22+ka33         = ka11+a22+a33         = ktrA{"version":"1.1","math":"trkA=trka11ka12ka13ka21ka22ka23ka31ka32ka33         = ka11+ka22+ka33         = ka11+a22+a33         = ktrA"}

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