2x2 Determinant Calculator

This calculator finds the determinant of a 2 by 2 matrix, one of the first calculations you meet when working with matrices in algebra, statistics or engineering. You enter the four entries of the matrix: a and b from the top row, and c and d from the bottom row. The calculator instantly returns the determinant, calculated as a times d minus b times c, and displays it alongside two extra results, whether the matrix is invertible (yes if the determinant is non-zero, no if it is singular) and the matrix laid out so you can double check what you typed. The determinant is more than a number to memorise; it tells you whether a matrix can be inverted, it measures how the matrix scales area when used as a transformation, and it underpins Cramer's rule for solving simultaneous equations and the vector cross product. A worked example is included below, using the matrix with rows (1, 2) and (3, 4), where the determinant works out to 1 times 4 minus 2 times 3, which equals minus 2. Use this tool to check homework, verify a hand calculation, or quickly test whether a matrix is singular before you try to invert it. Just make sure you enter each value in the right position, since swapping a, b, c or d around will change the result.

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