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Let A; B; C be square matrices of the same order n. If A is a non singular matrix; then `AB = AC` then `B = C` |
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Answer» If AB=AC=0 then it can be possible that B and C are two non-zero matrices such that `BneC` `therefore A.B=0=A.C` Let `A=[{:(1,0),(0,0):} ]B=[{:(0,0),(1,3):}]` and `C=[{:(0,0),(3,1):}]` `therefore AB=[{:(1,0),(0,0):}][{:(0,0),(1,3):}]=[{:(0,0),(0,0):}]` and `AC=[{:(1,0),(0, 0):}][{:(0,0),(1,3):}]=[{:(0,0),(0,0):}]` and `AC=[{:(1,0),(0,0):}][{:(0,0),(3,1):}]=[{:(0,0),(0,0):}]` `rArr AB=AC` but `BneC` |
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