A = a 2 15 31 12 b 2 41 35 61 c 2 and B = 2 a 3 5 2 2 b 8 1 4 2 c - 3 are two matrices such that the sum of…

Principal diagonal elements of $A$ and $B$ are $a^2, b^2, c^2$ and $2a, 2b, 2c-3$.

According to given condition, $a^2+b^2+c^2=2a+2b+2c-3$

$\Rightarrow \left(a^2+1-2a\right)+\left(b^2+1-2b\right)+\left(c^2+1-2c\right)=0$

$\Rightarrow {\left(a-1\right)}^2+{\left(b-1\right)}^2+{\left(c-1\right)}^2=0$$$

$\therefore a-1=0, b-1=0, c-1=0$

$\Rightarrow a=1, b=1, c=1$

Now, $\left(2a\right)\left(2b\right)\left(2c-3\right)$

Putting the values of $a, b$ and $c$ we get,

$=2\times 2\times -1=-4$