Multiplicative Inverses of Matrices and Matrix Equations
1 Find the Multiplicative Inverse of a Square Matrix
-$A = \left[ \begin{array} { l l } - 5 & 1 \ - 7 & 1 \end{array} \right] , \quad B = \left[ \begin{array} { l } \frac { 1 } { 2 } - \frac { 1 } { 2 } \ \frac { 7 } { 2 } - \frac { 5 } { 2 } \end{array} \right]$
A) $B = A ^ { - 1 }$
B) $\mathrm { B } \neq \mathrm { A } ^ { - 1 }$

Question

Quizplus · Accepted Answer

The multiplicative inverse of a 2x2 matrix $A = \left[ \begin{array} { l l } a & b \ c & d \end{array} \right]$ is given by $A^{-1} = \frac{1}{ad-bc} \left[ \begin{array} { l l } d & -b \ -c & a \end{array} \right]$. For matrix $A$, the determinant $ad-bc = (-5)(1) - (1)(-7) = -5 + 7 = 2$. Thus, $A^{-1} = \frac{1}{2} \left[ \begin{array} { l l } 1 & -1 \ 7 & -5 \end{array} \right]$, which matches matrix $B$.

Multiplicative Inverses of Matrices and Matrix Equations 1 Find the Multiplicative

Multiplicative Inverses of Matrices and Matrix Equations
1 Find the Multiplicative