Here is a short guide on how to square 2×2 matrix and calculations (also read as 2 by 2 matrix calculation). It is definitely multiplying that particular matrix by itself.
If the matrix defined in question is matrix A, then, the square of the matrix is represented by A² or matrix A.A
For example,
Given matrix A =[e f, g h]. Find the square of the matrix {A²}?
Solution
To multiply one matrix with another matrix, we do row by column calculations. For example we multipy row one of first matrix with column one of the second matrix .
(Take the first character in row one and then multiply with the first character of first column in the second matrix and add to the second character of row one in matrix one with the second character in matrix two column one.)
Hint: I presented the multiplication sign with a dot. for example; e.e represent (e) multiplied by (e).
The expression above shows calculations of a square of a 2×2 matrix.
Therefore, let’s solve another instance with values and see how to go about 2×2 matrix when you are required to work for its square.
Related: Are you familiar with determinant of 2 by 2 matrix? Check here
How to find the squire of a 2×2 matrix – Examples
Example 1.
If matrix M is given by [1 0, 2 3]. Calculate A²?
Hint: The question requires you to calculate for the square of the matrix M (matrix M multiplied by matrix M)
Solution
The final answer is equal to [1 0, 11 9]
Example 2: How To Square 2×2 Matrix – Calculations
If matrix W = [2 -4, 3 7]. Find A²
Therefore, the square of matrix W (a 2×2 matrix) given by W = [2 -4, 3 7] is [-8 -36, 27 37].
The formula to find a square of any matrix is definitely by working row by column calculations.
On the other hand, you can also check whether your answer was right by using this online matrix calculator here.
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