||A|=ad−bc Total case =64 For non-singular matrix |A|≠0⇒ad−bc≠0 ⇒ad≠bc And a,b,c,d are all different numbers in the set {1,2,3,4,5,6} Now for ad=bc (i) 6×1=2×3 ⇒
a=6,b=2,c=3,d=1
or a=1,b=2,c=3,d=6
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} 8 such cases (ii) 6×2=3×4 ⇒
a=6,b=3,c=4,d=2
or a=2,b=3,c=4,d=6
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} 8 such cases favourable cases =6C4!−16 required probability =