If A is a 2x2 matrix such that trace(A) = det(A) = 3, then what is the value of trace of (A-!) ?

Find the sequence of the elementary matrices whose product is the non singular matrix below. [2410]

Use an example chosen from 22 matrices to show that for nn matrices A and B,ABBA but AB=BA.

Can a matrix with an entire column of zeros have an inverse? Explain why or why not.

11. Find two nonzero matrices and such that.

In general, it is difficult to show that two matrices are similar. However, if two similar matrices are diagonalizable, the task becomes easier. In Exercises 38-41, show that A and B are similar by showing that they are similar to the same diagonal matrix. Then find an invertible matrix P such that .

Determine if the statement is true or false. If the statement is false, then correct it and make it true. For the product of two matrices to be defined, the number of rows of the first matrix must equal the number of columns of the second matrix.

True or false? det(A) is defined only for a square matrix A.

Find two 22 matrices such that |A|+|B|=|A+B|.