Question Video: Evaluating the Determinant of a Given Matrix Mathematics

Find the determinant of the following matrix. [5, 1 and −1, 5]

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Video Transcript

Find the determinant of the following matrix five, one, negative one, five.

We recall that the determinant of any matrix is written inside absolute value bars. The determinant of the two-by-two matrix 𝑎, 𝑏, 𝑐, 𝑑 is equal to 𝑎𝑑 minus 𝑏𝑐. The determinant of the matrix five, one, negative one, five is equal to five multiplied by five minus one multiplied by negative one. Five multiplied by five is equal to 25. Multiplying a positive number by a negative number gives a negative answer. Therefore, one multiplied by negative one is negative one. We know that subtracting negative one is the same as adding one. The determinant of the matrix five, one, negative one, five is therefore equal to 26.

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