Question

Let $A=\left[\begin{array}{ll}2 & -5 \\ 1 & -3\end{array}\right] \quad B=\left[\begin{array}{ll}4 & 3 \\ 1 & 1\end{array}\right] \quad C=\left[\begin{array}{rr}2 & 3 \\ -2 & 1\end{array}\right]$ a. Find $A B C, A^{-1}, B^{-1}$, and $C^{-1}$. b. Show that $(A B C)^{-1}=C^{-1} B^{-1} A^{-1}$.

          Let
$A=\left[\begin{array}{ll}2 & -5 \\ 1 & -3\end{array}\right] \quad B=\left[\begin{array}{ll}4 & 3 \\ 1 & 1\end{array}\right] \quad C=\left[\begin{array}{rr}2 & 3 \\ -2 & 1\end{array}\right]$
a. Find $A B C, A^{-1}, B^{-1}$, and $C^{-1}$.
b. Show that $(A B C)^{-1}=C^{-1} B^{-1} A^{-1}$.

Added by Chase H.

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Solved by Expert Hitendra Singh

Step 1

We can find the matrix products and inverses using the following formulas: Matrix product: $A B = \left[\begin{array}{ll}2 & -5 \\ 1 & -3\end{array}\right] \left[\begin{array}{ll}4 & 3 \\ 1 & 1\end{array}\right] = \left[\begin{array}{ll}-6 & -7 \\ -1 & Show more…

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Let $A=\left[\begin{array}{ll}2 & -5 \\ 1 & -3\end{array}\right] \quad B=\left[\begin{array}{ll}4 & 3 \\ 1 & 1\end{array}\right] \quad C=\left[\begin{array}{rr}2 & 3 \\ -2 & 1\end{array}\right]$ a. Find $A B C, A^{-1}, B^{-1}$, and $C^{-1}$. b. Show that $(A B C)^{-1}=C^{-1} B^{-1} A^{-1}$.