Question

If A and B are n times n matrices. Find the cost of calculating A^2+BAB

Matrices
ANSWERED
asked 2020-12-21
If A and B are \(n \times n\) matrices. Find the cost of calculating \(A^2+BAB\)

Answers (1)

2020-12-22
Step 1
According to the given information,
It is required to determine the cost of calculating \(A^2+BAB\)
where A and B are \(n \times n\) matrices.
Step 2
The cost of multiplying two square matrices of order \(n \times n \text{ is } n^3\)
cost of \(A^2=n^3\)
cost of \(BAB=(BA)B\)
cost of \(BAB=n^3+n^3\)
thus,
cost of \(A^3+BAB=n^3+n^3+n^3\)
cost of \(A^3+BAB=3n^3\)
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