Question

pls solve this quickly!​

Answer 1

Given,

$\sf{A}=\left[\begin{array}{ccc}-5&1&3\\7&1&-5\\1&-1&1\end{array}\right]$

$\sf{B}=\left[\begin{array}{ccc}1&1&2\\3&2&1\\2&1&3\end{array}\right]$

______________________________

(1)

$\sf{|A|}=\left|\begin{array}{ccc}-5&1&3\\7&1&-5\\1&-1&1\end{array}\right|$

$\sf{|A|=(-5)[(1\times 1)-(-1\times -5)]-1[(7\times 1)-(1\times -5)]+3[(7\times -1)-(1\times1)]}$

$\sf{|A|=[-5\times (1-5)]-[1\times (7+5)]+[3\times (-7-1)]}$

$\sf{|A|=(-5\times -4)-(1\times 12)+(3\times -8)$

$\sf{|A|=20-12-24}$

$\sf{|A|=-16}$

______________________________

(2)

$\sf{|B|}=\left|\begin{array}{ccc}1&1&2\\3&2&1\\2&1&3\end{array}\right|$

$\sf{|B|=1[(2\times 3)-(1\times 1)]-1[(3\times 3)-(2\times 1)]+2[(3\times1)-(2\times 2)]}$

$\sf{|B|=[1\times(6-1)]-[1\times(9-2)]+[2\times(3-4)]}$

$\sf{|B|=(1\times 5)-(1\times 7)+(2\times -1)}$

$\sf{|B|=5-7-2$

$\sf{|B|=-4}$

______________________________

(3)

$\sf{AB}=\left[\begin{array}{ccc}-5&1&3\\7&1&-5\\1&-1&1\end{array}\right]\left[\begin{array}{ccc}1&1&2\\3&2&1\\2&1&3\end{array}\right]$

$\sf{AB}=\left[\begin{array}{ccc}(-5+3+6)&(-5+2+3)&(-10+1+9)\\(7+3-10)&(7+2-5)&(14+1-15)\\(1-3+2)&(1-2+1)&(2-1+3)\end{array}\right]$

$\sf{AB}=\left[\begin{array}{ccc}4&0&0\\0&4&0\\0&0&4\end{array}\right]$

$\sf{|AB|}=4\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]$

$\sf{|AB|}=4\times 1$

$\sf{|AB|=4}$

______________________________

(4) I am not sure about this answer...

$\sf{|A|.|B|=|AB|}$

Here,

$\sf{|AB|=4}$

$\sf{|A|.|B|=4}$