Video: Finding the Inverse of a Two-by-Two Matrix

Find the inverse of the following matrix. A = 3, 3, 1, 6.

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Video Transcript

Find the inverse of the following matrix: 𝐴 equals three, three, one, six.

If we have a matrix 𝑎𝑏𝑐𝑑, its inverse will be one over 𝑎𝑑 minus 𝑏𝑐 times 𝑑, negative 𝑏, negative 𝑐, 𝑎. So 𝐴 inverse will be one over 18 cause six times three minus three because of three times one.

And now for our matrix, we would need 𝑑, which is six, then negative 𝑏, so that would be negative three, negative 𝑐, which would be negative one, and then 𝑎, which will be three.

And 18 minus three reduces to 15. So one 15 times six, negative three, negative one, three. That would be 𝐴 inverse.

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