The correct option is D 9
Let M=⎡⎢⎣a1a2a3b1b2b3c1c2c3⎤⎥⎦∴M⎡⎢⎣010⎤⎥⎦=⎡⎢⎣−123⎤⎥⎦M⎡⎢⎣1−10⎤⎥⎦=⎡⎢⎣11−1⎤⎥⎦
M⎡⎢⎣111⎤⎥⎦=⎡⎢⎣0012⎤⎥⎦⇒⎡⎢⎣a2b2c2⎤⎥⎦=⎡⎢⎣−123⎤⎥⎦,⎡⎢⎣a1−a2b1−b2c1−c2⎤⎥⎦ ⎡⎢⎣11−1⎤⎥⎦,⎡⎢⎣a1+a2+a3b1+b2+b3c1+c2+c3⎤⎥⎦=⎡⎢⎣0012⎤⎥⎦⇒a2=−1,b2=2,c2=3,a1−a2=1,b1−b2=1,c1−c2=−1⇒a1+a2+a3=0,b1+b2+b3=0c1+c2+c3=12∴a1=0,b2=2,c3=7
⇒ Sum of diagonal elements = 0 + 2 + 7 = 9.