Question
By means of matrix multiplication show that the product of each matrix in Problem 6-15 with its inverse in Problem 6-17 equals the identity matrix.
Step 1
Let's denote the matrix from Problem 6-15 as \( A \) and its inverse from Problem 6-17 as \( A^{-1} \). Show more…
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Miscellaneous problems
In Exercises $13-18,$ use the fact that if $A=\left[\begin{array}{ll}{a} & {b} \\ {c} & {d}\end{array}\right],$ then $A^{-1}=\frac{1}{a d-b c}\left[\begin{array}{rr}{d} & {-b} \\ {-c} & {a}\end{array}\right]$ to find the inverse of each matrix, if possible. Check that $A A^{-1}=I_{2}$ and $A^{-1} A=I_{2}$ $$ A=\left[\begin{array}{rr}{6} & {-3} \\ {-2} & {1}\end{array}\right] $$
Matrices and Determinants
Multiplicative Inverses of Matrices and Matrix Equations
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