If XA=(I-A)^2 where X, A and I are 2x2 matrices and A=bmatrix1 & 2\\1 & 4bmatrix, then, X, = Option 1: 2 A Option 2: 4/(, A, ) Option 3: A, ^2 Option 4: 2/(, A, )

Answer: 4/(, A, ). Solution: Here, A, =4-2=2 and I-A=bmatrix0&-2\\-1&-3bmatrix with determinant -2. Taking determinants in XA=(I-A)^2 gives, X, *2=(-2)^2=4, so, X, =2=4/(, A, ).

Algebra

Matrices & Determinants

Medium

core

If $XA=(I-A)^2$ where $X, A$ and $I$ are $2\times2$ matrices and $A=\begin{bmatrix}1 & 2\\1 & 4\end{bmatrix}$ , then $|X|=$

$2|A|$

$\frac{4}{|A|}$

$|A|^2$

$\frac{2}{|A|}$

✅ Correct Option: 2

Here $|A|=4-2=2$ and $I-A=\begin{bmatrix}0&-2\\-1&-3\end{bmatrix}$ with determinant $-2$ .

Taking determinants in $XA=(I-A)^2$ gives $|X|\cdot2=(-2)^2=4$ , so $|X|=2=\frac{4}{|A|}$ .

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CUET Mathematics Past Year Questions (Topic-Wise)

If $XA=(I-A)^2$ where $X, A$ and $I$ are $2\times2$ matrices and $A=\begin{bmatrix}1 & 2\\1 & 4\end{bmatrix}$ , then $|X|=$