Question 8.4.3: Using the Quick Method to Find a Multiplicative Inverse Find...
Using the Quick Method to Find a Multiplicative Inverse
Find the multiplicative inverse of
A=[−13−24].
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This is the given matrix. We’ve designated the elements a, b, c, and d.
A−1=ad−bc1[d−c−ba] This is the formula for the inverse of [acbd].
=(−1)(4)−(−2)(3)1[4−3−(−2)−1] Apply the formula with a = –1, b = –2, c = 3, and d = 4.
=21[4−32−1] Simplify.
=[2−231−21] Perform the scalar multiplication by multiplying each element in the matrix by 21.
The inverse of A=[−13−24] is A−1=[2−231−21].
We can verify this result by showing that AA−1=I2 and A−1A=I2.
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